  By using a classical Liouville-type model of two dimensional dilaton gravity
we show that the one-loop theory implies that the fate of a black hole depends
on the conformal frame. There is one frame for which the evaporation process
never stops and another one leading to a complete disappearance of the black
hole. This can be seen as a consequence of the fact that thermodynamic
variables are not conformally invariant. In the second case the evaporation
always produces the same static and regular end-point geometry, irrespective of
the initial state.
