The ability to locally engineer semiconducting structures enables the development of next generation nanoscale devices and photonics. Contrary to the widely used selective area epitaxy, an alternative approach for localized single crystal growth on noncrystalline substrates is presented. Individual growth positions are defined by topological design of an electrostatic field above the substrate guiding the material transport of unipolar charged molecules to the nucleation and growth positions. In this way, the topologically designed electric field imprints the geometrical pattern for graphoepitaxial crystallite growth. After nucleation, the growth evolves into vertical growth of three-dimensional high aspect ratio towers tipped with single crystal copper oxide. The demonstrated graphoepitaxial method allows for the facile growth of advanced 3D material structures on noncrystalline substrates.