  A model in which the massive dilaton is introduced by minimally extending the
two dimensional topological gravity is studied semi-classically. The theory is
no longer topological because of the explicit Weyl scale symmetry breaking. Due
to the dilaton the semiclassical stress-energy tensor gets renormalized and it
is shown how the gravitational background coupled to the the dilaton depends on
the dilaton mass as well as the renormalization mass scale, but not on the
Newton's constant.
