  A recently introduced real space renormalization group technique, developed
for the analysis of processes in the Kardar-Parisi-Zhang universality class, is
generalized and tested by applying it to a different family of surface growth
processes.
  In particular, we consider a growth model exhibiting a rich phenomenology
even in one dimension. It has four different phases and a directed percolation
related roughening transition. The renormalization method reproduces extremely
well all the phase diagram, the roughness exponents in all the phases and the
separatrix among them. This proves the versatility of the method and elucidates
interesting physical mechanisms.
