A Campos notebook Toshinori Yagi filled with everything he could dig up about the people who carried One For All before his student did. Its full title runs Previous Successor Quirks, Notes for Young Midoriya, and it exists because the power began handing Izuku abilities that were never his.
Toshinori Yagi keeps a notebook for his student, titled in full Previous Successor Quirks, Notes for Young Midoriya. Its subject is the line of people who held One For All before Izuku Midoriya took it.
The reason it exists is practical. One For All absorbs the Quirks of everyone who carries it and can surface them without warning, so Toshinori went digging, wanting Izuku to have an answer ready the moment a new ability appeared. He works in a Campos notebook, the same way Izuku works on his Hero Analysis for the Future.
Toshinori records whatever he can reach. Hero names sit beside real ones, followed by what each Quirk did and how it behaved, the shape of the person's life, and eventually the circumstances of their death.
The picture that came together was not the one he expected. None of the predecessors carried a particularly formidable Quirk, since anyone who did was tracked down and killed by All For One. Nor was there a deliberate line of succession before Nana Shimura chose him. The earlier holders simply fought All For One, died young for it, and pressed the power into the hands of whoever stood closest, waiting on the day it grew heavy enough to finish him.
The notebook is written for Izuku Midoriya, out of Toshinori Yagi's own research, and it has holes he could not close. The second and third users defeated him entirely, lost to the era they lived in and to Quirks with too many facets to pin down.
One gap he made himself. On learning that Hikage Shinomori, the fourth holder, had died at forty, All Might scratched out the cause of death. He had begun to suspect what One For All does to the people who carry it, and he was not ready to write that down where his student could read it.

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Nana Shimura held One For All immediately before Toshinori Yagi, later known as All Might, and chose him as her successor without any deliberate line of succession set up beforehand.
Toshinori Yagi's notebook, Previous Successor Quirks, records that none of the earlier One For All holders carried a particularly powerful Quirk, since anyone who did was hunted down by All For One, and information on the second and third users is missing entirely.
Previous Successor Quirks, fully titled Previous Successor Quirks, Notes for Young Midoriya, is a notebook Toshinori Yagi filled with research on the people who carried One For All before Izuku Midoriya.
Toshinori Yagi wrote Previous Successor Quirks because One For All absorbs and can unexpectedly surface the Quirks of everyone who has carried it, and he wanted Izuku Midoriya to have an answer ready when a new ability appeared.
Toshinori Yagi scratched out the cause of death for Hikage Shinomori, the fourth One For All holder who died at forty, after starting to suspect what the power does to its users and not being ready to write it down for Izuku Midoriya.
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