In this paper we give the asymptotic growth of the number of connected
components of the moduli space of surfaces of general type corresponding to
certain families of Beauville surfaces with group either \PSL(2,p), or an
alternating group, or a symmetric group or an abelian group. We moreover extend
these results to regular surfaces isogenous to a higher product of curves.Comment: 27 pages. The article arXiv 0910.5402v2 was divided into two parts.
This is the second half of the original paper, and it contains the
subsections concerning the moduli spac
