Twinning, polytypism, and polarity are important aspects in nanostructural growth since their presence can affect various properties of the as-grown products. The morphology of nanostructures grown via van der Waals epitaxy is shown to be strongly influenced by the twinning density and the presence of polytypism within the nanostructures, while the growth direction is driven by the compound polarity. With ZnTe as the model material, vertically aligned nanorods are successfully produced with variable cross-section and branched crystals (tripods and tetrapods) on only a single type of substrate. Van der Waals epitaxy contributes by relaxing the lattice-mismatch requirements for epitaxial growth and by enabling a variety of crystal planes in the initial stages of the growth to be interfaced to the substrate, regardless of the polarity of the epitaxial material. These results may provide more flexibility in tuning rationally the morphology of epitaxial nanostructures into other shapes with higher complexity by routine adjustment of growth environment.