  This paper investigates the evolution of collapsing FRW models with a scalar
field having the potential which arises in the conformal frame of high order
gravity theories, coupled to matter described by a perfect fluid with energy
density $\rho$ and pressure $p$, obeying a barotropic equation of state. The
solutions are shown to evolve generically to a singular state in a finite time
and they are used as sources for radiating objects undergoing complete
gravitational collapse. Although these singularities may be naked in some
special case, it is shown that generically a black hole forms.
