A trip to an isolated village to collect a quirk ends with All for One being turned into a sheep. When a shapeshifting dragon boy has to rescue him from malevolent spirits out to eat him, that's just embarrassing. Izuku claims to be his son from a past life, but All for One doesn't believe a word of it. He only cares about turning back into a human and returning home.
Eri summons all her courage to save a prisoner from Overhaul. Unfortunately, she saves All for One.
All for One strikes a deal with a demon to heal his wounds in exchange for his first-born son. He intends to scam the demon, since he never plans to have children. He forgot about his one night stand with Inko Midoriya many years ago.
In which Inko is every bit as family crazy as Hisashi/All for One, that's the basis of their entire relationship, and Izuku is the unfortunate target of the obsession of a yandere parent power couple.
After All for One was maimed during his fateful fight with All Might, Kurogiri accidentally gave the master's wife Inko the address to the villains' secret hospital. Izuku, convinced that his father was injured by the same villain who hospitalized All Might, launches an investigation with Tomura and Gigantomachia as his shanghaied sidekicks.
All for One took on the fake identity of David Shield in order to worm his way into All Might's confidence. He even went so far as to marry All Might and adopt Melissa just so he could one day force All Might to watch as he ripped off his daughter's fingernails one by one until the hero handed over his quirk. All for One never anticipated getting attached to the girl.
After convicting Hisashi Midoriya of being a deadbeat, Principal Nezu invokes an ancient U.A. tradition to find Izuku a new father. Both Izuku and his half a dozen potential fathers are roped into the Bachelor Dad Style whether they like it or not.
Izuku tries to study. The ghosts inside his quirk are not helping.
Shouto Todoroki has figured out that one of the students at U.A. is being haunted by seven and a half ghosts. Unfortunately, he thinks it's Hitoshi Shinsou. And he's recruited Izuku to help him make a video proving it.