  We study the effect of transport processes (diffusion and free--streaming) on
a collapsing spherically symmetric distribution of matter in a self--similar
space--time. A very simple solution shows interesting features when it is
matched with the Vaidya exterior solution. In the mixed case (diffusion and
free--streaming), we find a barotropic equation of state in the stationary
regime. In the diffusion approximation the gravitational potential at the
surface is always constant; if we perturb the stationary state, the system is
very stable, recovering the barotropic equation of state as time progresses. In
the free--streaming case the self--similar evolution is stationary but with a
non--barotropic equation of state.
