From BYU Studies Quarterly, volume 61, number 4.
It is clear that Joseph Smith’s inspired translation of the Book of Abraham was connected to the Egyptian papyri he acquired in summer 1835. However, less clear is the precise relationship between the Book of Abraham text and the papyri. There are three main theories, which are summarized in this episode: (1) Joseph Smith used the papyri fragments which survive today, (2) he used papyri that we no longer have, or (3) he worked without the aid of any of the Joseph Smith papyri.