We report multi-layer ZnO nanosheets obtained by annealing Zn polyhedral particles in pure O-2. The structure comprises a cluster core with side faces terminated with 50-nm-thick multi-layer sheets. The nanosheets were found to be (0001)-oriented single-crystalline wurtzite ZnO. By studying the early growth stages, it appears that the sheets form through a ripening process of dendritic ZnO nanostructures, during which the single-crystalline nature and crystallographic orientation are conserved. The ripening is promoted by the rapid oxidation of the Zn polyhedral microcrystals. We also show that appropriate modification of the oxidation process leads to the formation of well-defined dendritic nanowires. The optical properties (photoluminescence and Raman) of these nanostructured materials are discussed.