We study the dominant rational maps from a general surface in P^{3} to
surfaces of general type. We prove restrictions on the target surfaces, and
special properties of the rational maps. We show that for a small degree the
general surface has no such map. Moreover a slight improvement of a result of
Catanese, on the number of moduli of a surface of general type, is also
obtained.Comment: 19 pages, accepted in Advances in Geometr
