  We study a bi-parametric family of dilaton gravity models with constant and
negative curvature. This family includes the Jackiw-Teitelboim gravity and the
Liouville gravity model induced by a bosonic string. Furthermore, this family
is conformally equivalent to the hiperbolic dilaton models. We propose boundary
conditions in the Fefferman-Graham and in the Eddington-Finkelstein gauge. We
check the consistency of the asymptotic conditions by computing the entropy of
their black hole solution.
