Branched coverings of CP2 and other basic 4-manifolds

We give necessary and sufficient conditions for a 4-manifold to be a branched covering of CP^2 and sphere products, which are expressed in terms of the Betti numbers and the signature of the 4-manifold. Moreover, we extend these results to include branched coverings of connected sums of the above manifolds. This leads to some new examples of closed simply connected quasiregularly elliptic 4-manifolds.