Yoichi Shigaraki's power did exactly one thing: hand itself to somebody else. Too faint to register as an ability for most of his life, it was written off as Quirklessness until his brother forced Power Stock into him. The two fused, and the result became One For All, the one Quirk All For One could never take.
Registered as "Kosei" Fuyo, this Emitter ability belonged to Yoichi Shigaraki and carried no offensive or defensive application whatsoever. Transference was its entire purpose. All For One long assumed he had robbed his twin of something in infancy, back when neither could have remembered it, but the truth proved stranger: the power had never properly formed, sitting as an unformed speck that even his own stealing ability failed to detect.
Yoichi's frailty explains the weakness. Starved of nutrients in the womb by his stronger twin, he grew up sickly, and his Quirk Factor stayed correspondingly faint. When All For One forced Power Stock onto him as a cruel gift, the dormant ability swallowed it to compensate for what it lacked. That fusion produced One For All.
Handover runs through DNA. The recipient swallows a hair taken from the wielder, or a drop of their blood, and the ability changes owners. The wielder has to want to give it up, though the person receiving it never has to agree, and that condition of willingness is precisely why All For One cannot steal it. He tried on the fifth and sixth holders, Daigoro Banjo and En Tayutai, and the Quirk repelled his hand.
Because Quirk Factor types run in families, Bestowal shared its brother's talent for taking other abilities in, though passively through transfer rather than by conscious theft. All For One confirmed as much, noting it had taken Power Stock in and merged with it to cover the strength it was missing. The power appears to have evolved further under Izuku Midoriya, who learned to send along not merely itself but pieces of what it holds. Intent matters as well: a transfer made in hostility can wound the recipient instead of empowering them.
Yoichi remains the only original owner. After All For One killed him in a possessive rage, his blood landed on Toshitsugu Kudo, who inherited the freshly fused power without asking for it. Kudo came to realize, as did All For One, that Yoichi's will kept living on inside One For All. Pursued relentlessly, Kudo made deliberate use of the transference ability, handing the power off to an ally named Bruce, and the cycle of cultivating it and passing it to a successor ran on for generations.
Izuku Midoriya demonstrated the ability twice in unusual ways. Fighting Nine, he pushed One For All's stockpiled strength into Katsuki Bakugo while the core stayed behind; All Might first suspected Katsuki had blacked out before the handover finished, then concluded the Quirk itself had chosen to stay with a boy willing to surrender it. During the Final War, Izuku joined the earlier holders in forcing their powers, and themselves along with them, into Tomura Shigaraki to crack the leaden shell around his soul. It destroyed One For All, but Izuku reached the root of his enemy's hatred.
Yoichi Shigaraki's original Quirk was Quirk Bestowal, registered as "Kosei" Fuyo, an ability with no offensive or defensive use whose sole purpose was transferring itself to another person.
All For One forced Power Stock onto Yoichi Shigaraki, believing him Quirkless and hoping the sudden power would draw him into his reign of terror. Instead it fused with Yoichi's own Quirk Bestowal to create One For All.
Quirk Bestowal passes through DNA. The recipient ingests a hair or a drop of blood from the current wielder, though the wielder must be willing to give up the power for the transfer to succeed.
Quirk Bestowal can only be given willingly by its holder, and All For One's stealing ability cannot override that condition. He tried to take it from the fifth and sixth One For All holders, Daigoro Banjo and En Tayutai, and the Quirk repelled his attempts both times.
Quirk Bestowal was destroyed alongside the rest of One For All during the Final War, after Izuku Midoriya and the earlier holders forced their powers, and themselves, into Tomura Shigaraki to break through his hatred.
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