  In this work we consider a two-dimensional quantum black hole sourced by the
trace anomaly of a conformal field theory. By using holography, we are able to
prove that the black hole size is always proportional to the number of states
inside the black hole, a result that might be interpreted as a two dimensional
version of the Bekenstein entropy law. Finally, we also show that such a black
hole has a minimal size (a remnant). Extrapolating this result for higher
dimensions, we show that this would imply that the remnant has a size way
larger than the Planck length and is, therefore, always weakly coupled.
