DadMight

ToshiDeku is the family ship between Toshinori Yagi and Izuku Midoriya from the My Hero Academia fandom.

Canon
Izuku has always admired All Might since he was a small child and wanted to be a hero just like him. At their first meeting, All Might thought that Izuku was just a fan, but he started to acknowledge him when he jumped to save Katsuki from the Slime Villain. From that moment, he was touched by Izuku's bravery, how he puts himself in danger for the sake of others despite not having a Quirk. He then decided he would pass his powers to Izuku, feeling that he is the only one worthy enough to inherit his strength, and they started to share a feeling of mutual respect for each other. He himself even mentioned that he has no regrets passing One For All to Izuku.

All Might is his confidante, mentor, friend in and out of school, and they share a mutual respect for each other's heroism ideals. Izuku's admiration and respect for All Might is so great that he had trouble trying to attack All Might during the End of Term Test, and when he had no choice but to attack All Might with Katsuki's Grenade Bracer, Izuku apologized.

Toshinori started to open up to Izuku as he sees his growth, going as far as to reveal personal details about his past such as how he was Quirkless, his fight with All For One and his scarring as a result of that battle.

He continues to express his pride in his growth as a hero.

Fanon
On AO3, ToshiDeku is the second most written ship for Yagi and the sixth most written for Midoriya. It is related to their mentor/student relationship as well as a father/son relationship. It is very common to find stories where Yagi marries Midoriya's mother, Inko, as well as ones where Midoriya is All Might's biological son. Plots where Midoriya's mom dies and Yagi Toshinori ends up adopting him are also frequent.

The ship became extremely popular after Todoroki kept making comments how Midoriya was All Might's "secret-love child." He made the connections after noticing how similar Midoriya and All Might's quirk were, unbeknownst of him, that was because the quirks were one and the same.

Paternal Yagi Toshinori/All Might and DadMight are common tags used for this ship.

Fandom
FAN FICTION
 * Yagi/Midoriya tag on FanFiction.net
 * Yagi/Midoriya tag on FanFiction.net
 * Yagi/Midoriya tag on FanFiction.net