  A general homogeneous two dimensional dilaton gravity model considered
recently by Lemos and S\` a, is given quantum matter Polyakov corrections and
is solved numerically for several static, equilibrium scenarii. Classically the
dilaton field ranges the whole real line, whereas in the semi-classical theory,
with the usual definition, it is always below a certain critical value at which
a singularity appears. We give solutions for both sub- and super-critical
dilaton field. The pasting together of the spacetime on both sides of a
singularity in semi-classical planar general relativity is discussed.
