The vortex structure in the nanoscale ferroelectrics, similar to the vortex structure in magnetic nanostructures, is regarded as a toroidal order which is different from the common homogeneous polarization order. The finding of the vortex in ferroelectric nanostructures opens exciting opportunities for designing nanomemory devices (Naumov I. et al, 2004 Unusual phase transitions in ferroelectric nanodisks and nanorods, Nature 432, 737). From phase field simulations, we investigate the size-dependent polarization distribution in ferroelectric nanostructures embedded in a nonferroelectric medium. The simulation results exhibit that vortex structures of polarizations and single-domain structures are formed in ferroelectric nanodots and nanowires, respectively. Furthermore, a single-vortex structure is formed in the ferroelectric nanodots, if the aspect ratio of thickness to lateral size is less than a critical value, whereas the ferroelectric nanodots are in a multi-vortex state if the aspect ratio exceeds the critical value. When the aspect ratio approaches infinity, nanodots will become nanowires, in which polarizations are homogeneous. DOI: 10.1063/1.2917715  Applied Physics Letters 92, 162905 (2008)