One For All

One For All (ワン・フォー・オール) is a transferable quirk possessed by its main host Izuku Midoriya and was used by its previous main hosts Nana Shimura and Toshinori Yagi.

History
Long ago, a man with a quirk that could steal and distribute quirks forcibly gave his quirk-less 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. Like a torch, it is passed on from user to user. 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 will not 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 did not wish it. However, this does not mean One For All can not be forcibly passed on.

After One For All is transferred to the recipient, the previous One For All user can still use the "leftover embers" of One For All and thus can access One For All's power; however, these leftover embers will not last for long and the previous One For All will slowly run out of the embers, resulting in the previous user losing One For All completely. According to All For One, using these last embers continuously will rapidly increase the loss of the power. After All Might defeated All For One, the embers of One For All have burned out and he cannot even maintain his muscle form for more than an instant.

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 user's 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.

Nana Shimura
All Might's predecessor and the seventh successor of One For All. Little is known about Nana's proficiency with One For All other than she was not strong enough to bring down All For One.

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. It seems that after transferring the power, his ability to use One For All slowly diminishes and after his battle with All For One, Toshinori completely uses up the remaining leftover embers of the torch which is One for All. Although he can still transform for an instant, he cannot maintain his muscle form anymore and would revert back very quickly.

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. During his second fight with Katsuki, Izuku is now able to use 8% of One For All's power.

Toshinori's Techniques

 * Texas Smash (テキサススマッシュ): Toshinori throws a right punch with enough force that the wind pressure sends anything made of liquid flying away. This move is first used to save Izuku from the Sludge Villain.
 * Detroit Smash (デトロイトスマッシュ): Toshinori preforms that same attack as Texas Smash except this move is with a downward punch instead of a straight punch. The punch is powerful enough to create a shock wave large and powerful enough to clear the weather. This move is first used to save Izuku and Katsuki from the Sludge Villain.
 * Missouri Smash (ミズーリースマッシュ): Toshinori runs towards an enemy while keeping his hand flat and hits the enemy on the head while running past them. This move is first used against Trapezius Head Gear.
 * Carolina Smash (カロライナスマッシュ): Toshinori runs towards an enemy while keeping his hands in a cross position, then in a downwards cross chop to the enemies head. This move is first used against Shigaraki, but it is intercepted by Noumu, who withstood the full-force of the attack, seemingly unharmed.
 * New Hampshire Smash (ニューハンプシャースマッシュ): Toshinori blasts himself towards his enemy and smashes his body into the enemy, crushing and injuring the enemy with his great weight. This move is first used to propel himself at Izuku.
 * Oklahoma Smash (オクラホマスマッシュ): Toshinori whirls around while enemies have latched onto him, spinning with enough force that when they are released they are easily thrown through concrete. This move is first used against Noumu.
 * United States of Smash: Using all his power, Toshinori delivers a punch with massive power, enough to reverberate shockwaves. This move was first used against All For One.

Izuku's Techniques

 * Detroit Smash (デトロイトスマッシュ): The same as All Might's move, except Izuku does it in the form of an uppercut.
 * 5% Detroit Smash (5 パーセント デトロイトスマッシュ): Izuku activates One for All Full Cowl, then jumps into the air, and delivers an enhanced downward punch to the opponent. He has also used this move in the form a straightforward punch.
 * 100% Detroit Smash (100 パーセント デトロイトスマッシュ): Izuku activates One For All at 100% and delivers a straightforward punch to the opponent.
 * Delaware Smash (デラウエアスマッュ): Izuku flicks his finger to create a powerful shock wave. Doing this fractures said finger, limiting the time he can use this move without gravely injuring himself up to 10 times.
 * 1,000,000% Delaware Detroit Smash (1000000 パーセント デトロイトデラウエアスマッュ): Izuku uses One For All 100% and, boosted by his adrenaline, delivers a powerful smack with incredible force that blasts the opponent away. This move is powerful enough to overpower Muscular's Muscle Augmentation and incapacitate him.
 * One For All Full Cowl (ワン・フォー・オール フルカウル): This technique allows Izuku to activate 5% of One For All throughout his body, letting the power course and flow through him instead of concentrating it in one location. Activating this technique gives him enhanced strength, speed, mobility and agility. It also prevents him from breaking his bones when attacking.
 * One For All Full Cowl Shoot Style (ワンフォーオールフルカウル シュートスタイル): A fighting style of using One For All that deviates from All Might. Izuku realizing that just imitating All Might's style which has its special moves centered on his fists was not the best style for him and was actually causing more harm to his arms, he developed a new style that centers more on his legs with the help of his friends.
 * One For All 100%: A technique that allows Izuku to attack using the full power of One For All throughout his body.

Trivia

 * To date, all of the moves using One for All are named after states and cities 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 clench their buttocks and scream within their heart: "SMASH!".
 * So far every named user has had a number in their name somehow correlating to what number user they are. The 7th user is Nana which is Japanese for 7. Toshinori Yagi has the kanji for 8 in his name. Izuku Midoriya has ku which can mean 9 in Japanese.
 * One For All's name is an inversion of All For One, showing the differing philosophies between their wielders. The former emphasizes one using their power for the betterment of others while the latter is meant to selfishly hoard power for one's own sake.
 * One for All, together with its counterpart, All for One, may be derived from the popular motto of the titular heroes of the novel The Three Musketeers by Alexandre Dumas.

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Один за всех ONE FOR ALL