One For All

One For All (ワン・フォー・オール) is a Quirk used by Toshinori and Izuku Midoriya and formerly by Shimura.

History
Long ago, a man with a Quirk that could steal and distribute Quirks forcibly gave his Quirkless little brother a Quirk that stockpiles power. However, the little brother already had a Quirk with no effect other than that it could be transferred to another. The little brother's Quirk (that could pass itself on) and the Quirk given to him by his older brother (that stockpiles power) merged and became One For All. Thus, the little brother became the first user of One For All.

Description
All Might explains that One For All is the union of two Quirks: A Quirk that stockpiles power and a Quirk that could be transferred to others. This mutation was caused by the Quirk All For One.

One For All allows the user to access stockpiled power, which grants the user momentary superhuman strength at destructive levels, increased agility and superhuman speed.

One For All receives its name from the fact that it can be "inherited" by others. The method of inheritance and transference of One For All is done by the recipient ingesting the current One For All user's DNA as shown with All Might giving Izuku his strand of hair to ingest which allowed Izuku to inherit One For All. One For All won't transfer to a new recipient unless its user wishes it, thus One For All cannot be forcibly stolen. For example, the Hero Killer Stain ingested Izuku's blood but did not inherit One For All because Izuku didn't wish it. However, this does not mean One For All can not be forcibly passed on.

Proper usage of One For All requires intense and rigorous training of the body to prevent the successor from being torn apart from the raw power. Even with the training, the Quirk still puts intense stress on the users body (as when Izuku first used it, he broke his left arm and both legs).

However, it is unclear what the true nature of One For All is. When Izuku was about to lose his match against Hitoshi Shinsou, because of his Quirk, he feels the presence of multiple people coursing through his body and activated One For All to break free from Hitoshi's control. Izuku theorizes that since his Quirk is the "sacred torch that is passed down through the ages," those people that he felt were the lingering presence of those who had this power before him. He also mentions seeing someone with the same hair style of All Might among those who appeared in front of him, indicating that his presence is imprinted on the Quirk.

The first user
The first user of One For All was the little brother of a villain who had the Quirk All For One. One For All was formed from the mutation of the first user's innate Quirk and a Quirk given by his brother. The first user attempted to defeat his brother with his newly merged Quirk (now called One For All) but was not strong enough. He then passed One For All down to a successor in the hopes that someone would eventually stop his evil older brother.

Shimura
All Might's predecessor. Little is known about him.

Toshinori Yagi
As well-renowned hero All Might, Toshinori is a proficient user of this Quirk. He is capable of controlling his own strength and focusing his power into any extremity he chooses without recoil. However, due to an untreatable wound that has been inflicted on him, he can only utilize his power for three hours straight; any longer and it would strain his body. And if forced to use his Quirk more than he should, he may shorten the time limit for using his Quirk as a repercussion.

Izuku Midoriya
Izuku is the chosen successor of "One for All" by All Might. He has displayed incredible bouts of strength, but because of his inexperience in regulating his power, it usually results in the destruction of parts of his body. However, he is able to moderately distribute the power to specific limbs such as his fingers to limit the damage he does to himself. When he first used the power against another living being, he instinctively held back to avoid killing his opponent and from there was able to start learning how to properly modulate the output of the Quirk more efficiently, preventing the usual destruction of his body from happening at least on a subconscious level. Izuku's control of One For All and the power he can use is limited, as he can only use around 5% of his potential power safely according to All Might. In spite of that, there are times when he still unleashes the full 100% regardless of the damage to his own body, like when Izuku created wind pressures that are powerful enough to have shattered Shouto Todoroki's ice in order to force his rival to stop holding back or in case of emergencies. During his training with Gran Torino, he finally learned how to properly use One For All and developed a technique called "One For All Full Cowl" which allows him to use the 5% of One For All throughout all of his body to slightly enhance his strength, speed, and agility.

Trivia

 * To date, all of the moves using One for All are named after states in the USA (e.g. Missouri Smash, Delaware Smash). This is consistent with the manga artist's desire to model All Might after American comic book heroes, especially in All Might's hero form.
 * According to All Might, to activate One For All, the user must scream: "SMASH!"
 * One of the reasons why Deku has so much problems with handling the Quirk is because All Might is clueless regarding how to help Deku in developing it safely due to him having an intuitive grasp of how to control it, something that his apprentice doesn't have.

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Один за всех ONE FOR ALL