In this paper the authors study generic covers of C^2 branched over x^n + y^m = 0 s.t. the total space is a normal analytic surface. They found a complete description of the monodromy of the cover in terms of the monodromy graphs and an almost complete description of the local fundamental groups in case (n, m) = 1. For the general case, they give explicit descriptions of base changes in terms of monodromy graphs; they describe completely the embedded resolution graphs in the case n|m. Via these base changes every cover is a quotient of such a cover.