Our main goal is to explore complex surface geography through the geography of arrangements of Riemann surfaces on complex surfaces. For that, we have a method which associates to a given suitable arrangement a sequence of complex surfaces. These new 4-manifolds have Chern numbers asymptotically proportional to the ones of the arrangement. I will explain the method, and the geography of some families of arrangements, which are analogues of line arrangements in the projective plane. Several open problems will be described.