The growth behavior of cadmium chalcogenides (CdE = CdS, CdSe, and CdTe) on sphalerite Cu(2-x)Se nanocrystals (size range 10-15 nm) is studied. Due to the capability of Cu(2-x)Se to undergo a fast and quantitative cation exchange reaction in the presence of excessive Cd(2+) ions, no Cu(2-x)Se/CdE heterostructures are obtained and instead branched CdSe/CdE nanocrystals are built which consist of a sphalerite CdSe core and wurtzite CdE arms. While CdTe growth yields multiarmed structures with overall tetrahedral symmetry, CdS and CdSe arm growth leads to octapod-shaped nanocrystals. These results differ significantly from literature findings about the growth of CdE on sphalerite CdSe particles, which until now had always yielded tetrapod-shaped nanocrystals.