ZnO ultrathin films supported on Cu, Ag or Au are attracting increasing interest because they can form under special conditions on commercial Cu/ZnO/Al2O3 catalysts for methanol synthesis, or can be used as alternative materials for catalysis, or as prototypes of the so-called inverse catalysts. In the present study, we have investigated the thickness dependence of the structure and electronic properties of free standing and Cu(111) supported ZnO ultrathin films by means of DFT+ U calculations. On the free-standing films, a flat graphitic-like morphology is observed up to 10 layers, where a transition to wurtzite-like structures occurs. On Cu(111), a slightly corrugated graphitic structure is obtained for ZnO films up to 4 layers. From 5 layers on, the rumpling becomes substantial and a phase transition to wurtzite takes place. The driving force behind the destabilization of flat graphitic films on Cu(111) is the charge transfer from the underlying Cu support to the film. This finding rationalizes the experimental observations that the transformation from graphitic to wurtzite polymorph of ZnO films on Cu takes place above 5-layer thickness.