Metal oxide nanostructures and thin films grown on metallic substrates have attracted strong attention as model catalysts and as interesting inverse catalyst systems in their own right. In this study, we investigate the role of metal support in the growth and stabilization of cobalt oxide nanostructures on the three related (111) surfaces of Au, Pt and Ag, as investigated by means of high-resolution Scanning Tunneling Microscopy (STM) and DFT calculations. All three substrates promote the growth of crystalline CoOx (x=1-2) islands under oxidative conditions, but we find several noteworthy differences in the occurrence and stabilization of four distinct cobalt oxide island phases: Co-O bilayers, O-Co-O trilayers, Co-O-Co-O double bilayers and O-Co-O-Co-O multilayers. On atom-resolved images combined with analysis of lattice dislocation lines in bilayer islands on Au and Pt, we furthermore unambiguously determine the edge structure. Interestingly, the island shape and abundances of edge types in bilayers change radically from mixed Co/O edge terminations on Au(111) to a predominance of Co terminated edges (~91%) on Pt(111) which is especially interesting since the Co metal edges are expected to host the possible active sites for water dissociation.