We report on the epitaxial growth of ZnO nanosheets and nanowires on a- and c-plane sapphire substrates by Au-assisted pulsed laser deposition. The epitaxial relationship of the nanostructures was determined by x-ray diffraction (XRD) pole figure measurements. On c-plane sapphire, the ZnO nanowires grew along the ZnO c-axis and were inclined to the substrate surface normal with an angle of about 37°. The ZnO(0001) plane of the wires aligned with of the sapphire substrate via two degenerate in-plane configurations, promoted by low lattice mismatch (0.05%). ZnO nanosheets grown on c-plane sapphire exhibited no preferential orientation on the substrate and no epitaxial relationship could be unambiguously identified. On a-plane sapphire, ZnO nanowires grew vertically along the ZnO c-axis with a single epitaxial configuration, whereas ZnO nanosheets seemed to grow along in two preferred in-plane orientations, 72°–74° apart. These configurations could be explained by two distinct alignments of the plane on the a-plane sapphire substrate surface, promoted by low lattice mismatches.