Decay was Tomura Shigaraki's defining weapon: a touch that reduced anything it found, living or otherwise, to dust. All For One slipped it into him at five years old and let him believe it was a freak mutation, and it grew alongside his hatred until it could erase most of a city.
Given as Hōkai in Japanese, this contact-range Emitter Quirk appears in Chapter 16 and Episode 11. All For One held it before passing it on, and Tomura Shigaraki carried it for the rest of the story. Anything his hands found crumbled away, and the distinction between organic and inorganic meant nothing to it, so flesh simply rotted off a victim who was struck.
Speed was the variable. Early on the disintegration took several seconds, and against a person it would work its way through the whole body unless the affected limb came off, a fate Eraser Head avoided by cancelling the effect with Erasure before it could spread. As Tomura developed, the process shortened to nearly instantaneous and the spread stopped respecting the point of contact, running outward into a chain of victims who had never been touched at all.
The origin was a lie. Everyone took the Quirk for a rare mutation nobody had anticipated, but it was in fact a reverse-engineered duplicate of Kai Chisaki's Overhaul. The original carried a restorative half alongside the destructive one, and Kyudai Garaki stripped that half out before All For One quietly transferred what remained. The differences ran deeper than the missing restoration: Decay spread to whatever was connected to its target while Overhaul stayed contained, Decay could only be stopped by mutilation while Overhaul's effects were instant and localised, Decay left dust where Overhaul blew a body apart, and Decay initially demanded all five fingers where Overhaul needed only one.
Touch was the gate, so anything that denied contact denied the Quirk. Gloves shut it off completely, and opponents who could turn themselves to fluid or particles, as Snatch did with Sandstorm, gave his fingers nothing solid to find. Destroying or severing the affected area before the spread finished also worked.
Pushed hard enough it turned on its owner. Driven to its limit, the disintegration could rebound, which it did during the Revival Celebration at its peak, crawling up Tomura's own arm and leaving it bloodied and scarred. After Garaki's surgery grafted All For One into him and completed his body, the Quirk grew potent enough to slowly consume him anyway, showing up as cracks across his face and skin.
His Quirk Factor sat in his hands, specifically the fingers, so losing them would have cost him the power much as it would have cost Chisaki. The Final War made that moot: Super Regeneration plus the Quirk Singularity gave him huge appendages studded with fingers, extending Decay's reach on a far worse scale. He also had discretion over what he ruined, sparing X-Less's cape while disintegrating the hero wearing it and leaving intact most Near High-End Nomu housed in Garaki's lab, though not all of them. Its reach even extended past matter into spirit, letting him destroy the vestiges of his family and tear at All For One's vestige, and, when Izuku invaded his soul, tear off Izuku's arms with damage that persisted after he woke.
All For One held the modified copy first and engineered its transfer. He planted it in five-year-old Tenko Shimura while walking him home, and days later it went off for the first time as the boy played with his dog Mon. A shock ran through Tenko's left arm just before his father struck him; embracing Mon triggered it; the dog died, then his sister Hana, and finally, resentful and unravelling, Tenko took the rest of his family and the house with them. As a child the effect was cruder, leaving chunks rather than dust. All For One used the aftermath to collect the orphan as his pupil and successor, and had the hands of the dead salvaged so Tomura could carry them as keepsakes that kept his rage and hatred fed, exactly as the plan required.
Tomura Shigaraki spent years unaware of what he actually had. His memories of the massacre were repressed, and with them the knowledge that his Quirk could spread through a household, so he unconsciously held himself short of his real capacity until damage to his family's preserved hands during the Revival Celebration began forcing the past back up. Fighting the Meta Liberation Army, he relearned the ability in real time. Decay was always his primary method, forcing him into close quarters, though contact alone was usually enough to kill or maim. He kept one finger raised off objects and hostages he wanted intact, promising to dust them the moment they refused him, a discipline that lapsed whenever he lost his temper.
Weeks of combat against Gigantomachia sharpened it further, cutting the delay to nothing and letting it keep evolving under stress. Even with his left hand half destroyed he decayed part of Re-Destro's index finger using two remaining digits, slower and weaker than a full grip. By the end of that fight the Quirk had turned solipsistic, taking anything connected to whatever he touched, and could turn most of a city into an ash cloud, at the cost of an arm left heavily scarred. After the All For One graft removed the backlash, he could seed the spread by resting a hand on the floor, which is how Jaku General Hospital and the city around it went. During the Final War he aimed the destruction downward into the earth's crust instead of outward, dropping a large stretch of Shizuoka Prefecture and letting the tides take it. When All For One finally destroyed what was left of Tomura's spirit and reclaimed the body, he observed that Decay had gone out with the rage and hatred that fed it.

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Decay is a contact-range Emitter Quirk that reduces anything it touches, living or not, to dust. Tomura Shigaraki carried it for most of the series after All For One secretly implanted it in him as a child.
Yes, Decay is a reverse-engineered duplicate of Kai Chisaki's Overhaul quirk. Kyudai Garaki modified the copy to strip out Overhaul's restorative half, leaving only the destructive disintegration effect.
No, Decay was not a natural mutation as everyone believed. All For One secretly implanted the reverse-engineered Overhaul copy into five-year-old Tenko Shimura, letting him grow up thinking it was his own rare power.
No, Decay was never held by Izuku Midoriya. It passed only from All For One to Tomura Shigaraki, and Izuku instead fought against it as one of Tomura's opponents.
Decay activates through touch and disintegrates whatever it contacts into dust, without distinguishing between living tissue and inanimate objects. Only gloves, severing the affected area, or turning to fluid or particles could deny the quirk a solid target to destroy.
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