Beauville surfaces, moduli spaces and finite groups

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 spaceIn 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