  Boundary actions for three-dimensional quantum gravity in the discretized
formalism of Ponzano-Regge are studied with a view towards understanding the
boundary degrees of freedom. These degrees of freedom postulated in the
holography hypothesis are supposed to be characteristic of quantum gravity
theories. In particular it is expected that some of these degrees of freedom
reside on black hole horizons. This paper is a study of these ideas in the
context of a theory of quantum gravity that requires no additional structure
such as supersymmetry or special gravitational backgrounds. Lorentzian as well
as Euclidean regimes are examined. Some surprising relationships to Liouville
theory and string theory in AdS(3) are found.
