Ai grew up in the rundown town called Hole, where sorcerers came to hone their magical powers by experimenting on humans.
Though Hole was basically an anarchistic society, a vigilante militia sprung up to fight the sorcerers, leaving their bodies to rot or burn in the streets. Haze (Dr. Kasukabe) scavenged such bodies and brought them to his lab. Studying sorcerers and their anatomy was a passion of his. His wife was a sorcerer, and he even wrote a book on the subject.

Ai read this book and sought out Haze to learn more about sorcerers. He examined their bodies and got familiar with the devil tumors that held the key to their magic. His greatest desire was to become a sorcerer himself.

Haze told him this was impossible, and Ai acknowledged his opinion, but he didn't give up, and privately kept researching the idea. His work appears to have even attracted the attention of Devils. And, finally, his determination paid off. A way was possible, incredibly convoluted though it was.
devil tumors
It called for the synergistic effect created by a special combination of materials, and one day Ai got his chance.

A sorcerer was drowning in one of Hole's many toxic lakes. It was full of chemical waste, sewage, sorcerer corpses, and rain water filled with magic smoke particles.

This thick, bubbling sludge was the secret ingredient to make Ai's method work.
sludge lake
This toxic sludge was extremely dangerous. When Haze saw how far the sorcerer was from the shore, he resigned to let him go.

But Ai fixated on the sludge. Though he knew it would mean death for his human body, the method he devised could be able to reconstruct him as a sorcerer, and he was willing to risk his life for that.

To Haze's horror, Ai dove into the sludge.

It peeled his skin and ate through his organs, but he managed to pull out the drowning sorcerer.

Haze brought both of them to his hospital.

When he asked Ai why he would do such a thing, he was shocked to learn that Ai had planned it all out. Indeed, Ai directed Haze to his personal notes detailing the surgery he wanted him to perform using the sorcerer's fresh body parts.

Haze didn't think it would work, but he did it anyway as a favor to (what he thought was) his dying friend.
Recovery 1
And Ai survived. He wasn't entirely the same person, and of rather questionable sanity, but he survived. The question is: how?
Sewer Water
Haze was right. It is impossible for a human to become a sorcerer. And, if the workers at the CrossEyes lab are any indication, it's also impossible for sorcerers to become like Ai, no matter how closely they follow his instructions. Ai became something like a magic user after the surgery, but only because he was no longer an ordinary human after jumping into the toxic sludge. He mutated into something else, and this allowed his body to be receptive to the surgery.

Hole's rain carries very special properties. The smoke particles from sorcerers experimenting in Hole drift up and accumulate in rain clouds. As such, the droplets are filled with pure magic, which has some bizarre effects on the world. When the rain falls, the water drains into the sewers, mixing with chemicals and corpses, a mixture quite similar to the sludge that Ai dove into. So, really, Ai isn't much different from Johnson, the giant cockroach whose mutation Caiman attributed to water pollution.

Ai was found dead in a gutter the day after leaving the hospital, rain water pouring into his face and upper torso. It was so corrosive it melted his face and seeped into his body. But Ai didn't stay that way. This is another effect of Hole's rain: it could raise the dead. So Ai is not just a mutant with body alterations. He's a mutant zombie.
Sewer water in face
It was believed he was killed by sorcerers, and the official cause of death was listed as "magic-induced suffocation." But, technically, he suffocated when redundancies in bones and tissues put pressure on his trachea. The autopsy uncovered that he had body alterations, and assumed the redundancies were the result of some substance-increasing magic. But were they really? Ai had body alterations of his own, and perhaps already made redundant parts, such as his multiple heads. Was he trying to switch heads and suffocated from the pressure of one trying to come out of his neck?

This most likely happened before Ai acquired the special dimension he has inside himself to compactly store large stuff. High concentrations of smoke particles can actually warp space and make you see illusions. They turned Haze's laboratory into an endless maze filled with apparitions. The rain water that inundated Ai's face and seeped into his torso created a spatial distortion in the upper half of his body. It was inhabited by Ai, who was later joined by Curse. Anyone whose head was bitten by Caiman also entered it, even while their full body remained in the outside world.
The dimension also had other apparent residents, all of them headless at the neck (as opposed to torso like Ai was). It's unclear who they are.

It's possible that they're Kai's beheaded victims whose souls are trapped in the dimension because Kai had their devil tumors in his head. However, the old Kai's head - the one which presumably had all the devils - got torn off by Curse. It's possible that Kai switched to an empty head just in case, but the reborn Kai didn't appear to have any extra magical abilities. He kept using the mushroom magic he stole from En after coming back, which points to him having lost his old powers, so there'd be no devils to bind those souls to him at the time we see that scene.

I've also thought that maybe they're magic users whose parts Ai used to modify his body. But I tried to match the clothes of the sorcerer drowning in the sludge lake to any of the people in the dimension to no avail. It's most likely they are illusions.

Ai's dimensional distortion is split into two parts: the "head" dimension and the "headless" dimension, with a floor and ceiling of sludge, respectively. Both halves serve as storage for Ai's bodies.

The head dimension is a tiled room which looks like Kai's old apartment. Only Ai's own bodies inhabit this place. They appear from mid-torso up, and their bottom halves are filled with a bubbly liquid - maybe sludge. There are tubes hooked into the liquid that connect to the sludge on the floor. This could be a way for Ai to transfer things, such as body parts, between the head and headless dimensions. When Ai is switching heads, this room completely fills up with sludge. This is reflected in Ai erupting in a sludge geyser outwardly, too. It's probably why there is sludge bubbling inside his neck and why his heads are covered in sludge when they emerge.

The headless dimension has rooms and tunnels whose walls look like they're made of organic material. It also houses Ai's bodies, but they're kept in sludge-filled crates. In fact, maybe sludge as a barrier between the head and headless dimensions isn't accurate. Maybe it is the sludge in these crates that creates the head dimension. The headless dimension links directly with Ai's outward body, and traveling through it's tunnels leads up his throat and into his mouth. So perhaps the ceiling sludge marks a point in the outward body's neck, and the tubes from the head dimension connect to it, acting like a sludge faucet through which the heads emerge.
Head & Headless Dimensions
Horrible Dream
Emerging from Crates
Just as Ai's heads exit into the outer world from the head dimension, his aspects enter the dimensional distortion from the sludge inside the crates. But they enter it whole, not headless. Likewise, when Ai comes to the head dimension, he doesn't gain a head. His melted head is there already, standing as one of the bodies.

Perhaps, then, these aren't "head" and "headless" dimensions at all. The headless people are apparitions of sorcerers Kai killed that still psychologically haunt him, and Ai is missing the top half of his torso because that part - permeated by rain water - is being used to create the entire distortion. It's not gone. It's ambient!

Ai took steps to ensure that he'd survive long enough to accomplish his ultimate goal. He basically has 9 lives. The 9 crates contain not only his 9 heads, but 9 whole bodies.

After the original Kai was decapitated by Curse, that body was missing a head (far left). The fact that he kept the headless body anyway indicates that he could still use it for spare parts when the outer body gets injured. This is in contrast with Caiman's confrontation with En. En destroyed Caiman's whole body with mushrooms from inside out. That body died. Even Curse thought so and left. Kawajiri commented how it was cold and not breathing. There were no parts left to use, and this was reflected in the distortion with the breaking of Caiman's crate, leaving nothing but sludge and bones.

Though Ai's use of his spare parts can account for his outer body's remarkable healing abilities, once a part is gone, he can't regenerate it. The heads torn off by Curse and Shin are just stumps of vertebrae now, and the head that was cut in half remains so. What's interesting is that these losses are also reflected as diminishment in the mass of Ai's outer body. In this height chart, Caiman has a halo (because he's dead), but the new Aikawa is shown separately and shorter than him!
Rain Power
Ai's inner distortion is big enough to contain his own version of Hole. It's a city-scape of perpetual rain, and this is reflected in Ai's one innate power: rain aura. He can turn it on and off at will.

Hole's rain is the bane of all sorcerers. It fills them with pain and makes them sick. Ai doesn't hesitate to use it against them to gain an upper hand, allowing him to make short work of even someone as powerful as En.
Rain Power
Of course, Ai wanted more and more power. He wanted to become the ultimate magic user - and beyond.

As Kai, he hunted down sorcerers with powers he desired. He lopped off their heads, cut out their devil tumors, and surgically transplanted them into his own brain. He was skilled enough to perform these operations on himself, and had amassed quite a number of devils - along with the magic they possessed.

His greatest nemesis was En. Just as the original Kai was about to take En's head, he started experiencing technical difficulties and began the process of switching heads. This shut off his rain aura and allowed En to unleash enough of his smoke to turn an entire town into mushrooms. Yet Kai wobbled off unaffected and escaped through a magic door.

This could be explained by the fact that, when Ai switches heads, a whole lot of sludge shoots out. This sludge is made in large part of magic smoke particles from the rain. During Kai's battle with Fukuyama, it was shown that smoke can deflect other magic smoke, so it's possible that En's magic was repelled by the sludge that erupted from and covered Kai's body. 
Oil Blood
And Ai had a seemingly endless supply of sludge inside his body. Kai had a peculiar tendency to disappear from his chambers, leaving a puddle of the stuff on the floor. One'd think that their Boss leaking a dark, oily, and quite flammable liquid would raise some red flags for his CrossEyes followers, but nope. I suppose nothing is too strange in the sorcerer world.
Oil Vomit
They didn't have much issue with Kai having 8 more heads than he should, either. They were pretty surprised, but not bothered.
Ai's dream had evolved as he did. He no longer wanted to be a mere sorcerer, or even just a collector of magical powers. He wanted to transcend both sorcerers and humanity, to become a completely new being. To achieve his, he amassed an obscene amount of sorcerer corpses and was using the black powder from their devils to create an elaborate biological super suit.
Super Suit
When the time was right, Ai launched the final phase of his transformation. He recreated the lake of toxic sludge on a grander scale. He had the toxic waste inside him, he buried himself in the mountain of corpses, now he just needed rain.

It never rains in the sorcerer world, but Ai made full use of his power. He began to dismantle his dimensional distortion. First he released all the rain he had by purging the replica of Hole. As the distortion broke down, Ai's upper torso was visible on him again. He then summoned Aikawa back to him and collapsed everything - all the inner dimensions.

The crate housing Ai's original body shattered, and the rest of the crates were sucked into a chaotic whirlpool of sludge.

This overall inner fusion was reflected in the fusion of his outer body with itself and with the super suit. What emerged was a giant, four-faced monstrosity that breathed magic smoke and leaked concentrated black powder.

I call it Darth Kai since it makes Darth Vader-like respirator noises. But this creature couldn't walk or talk. Though it cast a magic door on instinct, it couldn't judge its relative size. Despite oozing magical power, it didn't know how to defend itself and mostly sat dormant in a corner. As Ai predicted, his old identity was completely gone. Darth Kai acted like a baby precisely because it was a newborn being.

The transformation didn't fail to draw in a crowd of Devils. Chidaruma, the King of Devils himself, was intrigued. And it seems that the Devils have been keeping an eye on Kai for a while now. Chidaruma didn't intervene to save his friend En. Haru kept warning Haze to stay away from Ai and, after the transformation, commented that there's no way to save Ai anymore and that she has her own job to do. The Devils' involvement in Ai's work is still a mystery.
Final Plunge
Darth Kai

What Ai created was essentially an artificial Devil. But, just as the artificial sorcerer he changed himself into wasn't identical to natural sorcerers, it stands to reason that the Devil he changed himself into isn't the same as the exiting Devils either.

The sorcerer body which Ai engineered was in many ways superior to natural sorcerers. It could gain powers by incorporating other devil tumors into its brain - something the CrossEyes at Kai's lab couldn't get to work on themselves. And, of course, the body came with a lot of spare parts and failsafes.

Is the Devil Ai engineered likewise superior to its natural counterparts? At first, it didn't seem so. The cumbersome body was all powered up with nowhere to go. But the transformation was not complete. In the language of evolution and mutation, Darth Kai was a transitional form (*smirk*). Right after the fusion of his body in the magic user world, he indicated that he needed to get to Hole to continue.

Ai needed more sacrifices and Hole's native sludge to attain his goal. Perhaps, even more specifically, he needed the same sludge pit he originally dove into.

Like a newly-hatched larva, Darth Kai was terribly hungry. He devoured the dead bodies around him through tubes and deposited them into a huge bag attached to his back. Once he gathered enough corpses, he mixed them with the devil tumors he collected before, and dove into the sludge pit.

This allowed him to metamorphose into a more human-looking form. He advanced through a tunnel followed by a wall of sludge, chanting "Hole." His speech bubbles were now spiky like a Devil's.
Is this Ai's final form? He has shown another form: that of a pure sludge monster strewn with heads and spikes. Was this a hallucination? He has triggered at least one hallucination lately... or was that a premonition? Perhaps it's an effect of the sludge... but is Ai separate from the sludge? Is he now the humanoid figure or the wall of sludge... both?

The surge of sludge inside Ai may have affected the functioning of his inner dimension. After getting killed by Darth Kai, Ton found himself in a deserted city, filled with buildings and roads. This was not Hell, where sorcerers normally go upon death.

Until now, we've only seen the dimension from inside Ai's headquarters, since that is where his various aspects enter/exit from/to the outer world. However, from the windows of the headquarters, it could be seen that Ai had a whole replica of Hole inside him. Not being one of Ai's aspects, did Ton simply end somewhere in that greater city? Or did Ai's inner dimension actually change?

Unlike the headless ghosts haunting Ai's headquarters, Ton retained his head, as did Natsuki who he pulled out of a sludge pit. Both of their devil tumors had been absorbed by Darth Kai. This was very different from what happened to En. En's devil tumor was incorporated by sorcerer Kai, but En still ended up in Hell.

Could the concentration of sludge inside Ai be so great, and twisting space to such an extent, that it is acting as a black hole which won't even let souls escape? Ton and Natsuki were trapped in a reality distortion which circles in on itself.
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DISCLAIMER: all story, art, characters are copyright Q Hayashida. This is a fansite. No copyright infringement is intended. Translations by Gantz Waiting Room, VIZ Media, and sometimes myself. Dorohedoro is published in Ikki Magazine.