First principle calculations are used to determine the relative stability of wurtzite and graphitic phases of ZnO nanostructures. Our results indicate that the relative stability sequence changes with the increasing size of the nanostructure. When the number of ZnO molecules in the ZnO nanostructure is less than a threshold number, we observe the relative stability of the graphitic phase. When the number of ZnO molecules in the ZnO nanostructure exceeds the threshold number, the relative stability of the wurtzite phase is observed. Finally, we discuss the influence of size dependence of these ZnO nanostructures on their electronic properties. (C) 2008 Elsevier B.V. All rights reserved.