Superconducting critical temperatures Tc are calculated as a function of the doping parameter x for generic layered Cu oxide superconductors, within the framework of a 2D-XY model with quantum phase fluctuations. The model accounts for the lower doping threshold observed at x=0.05, and allows for a simple interpretation of the ‘‘pseudogap’’ in terms of condensation of pre-formed pairs. On the other hand, a novel pairing mechanism, based on the 2D confinement of carriers and on the in-plane overscreening of long-range Coulomb repulsion, is proposed. A 2–3D dimensional crossover which suppresses 2D pairing is considered in the overdoped regime