Does anyone have a copy of Schlessinger's Thesis (not his paper "Functors of Artin Rings")
As other posters have mentioned, this document is cited in Deligne-Rapoport's "Les schemas de modules de courbes elliptiques" and Deligne-Mumford's "The irreducibility of the space of curves of given genus" and from what I can tell used in essential ways beyond what appears in "Functors of Artin Rings".