The Collaborative International Dictionary of English v.0.48:

Papaw \Pa*paw"\, n. [Prob. from the native name in the West
   Indies; cf. Sp. papayo papaw, papaya the fruit of the papaw.]
   [Written also pawpaw.]
   1. (Bot.) Same as papaya, senses 1 and 2.
      [1913 Webster +PJC]

   2. (Bot.) A tree of the genus Asimina (Asimina triloba),
      growing in the western and southern parts of the United
      States, and producing a sweet edible fruit; also, the
      fruit itself. --Gray.
      [1913 Webster]

WordNet (r) 3.0 (2006):

Asimina triloba
    n 1: small tree native to the eastern United States having
         oblong leaves and fleshy fruit [syn: pawpaw, papaw,
         papaw tree, Asimina triloba]