By studying the time-dependent axial and radial growth of InSb nanowires (NWs), the conditions for the synthesis of single-crystalline InSb nanocrosses (NCs) by molecular beam epitaxy are mapped. Low-temperature electrical measurements of InSb NC devices with local gate control on individual terminals exhibit quantized conductance and are used to probe the spatial distribution of the conducting channels. Tuning to a situation where the NC junction is connected by few-channel quantum point contacts in the connecting NW terminals, it is shown that transport through the junction is ballistic except close to pinch-off. Combined with a new concept for shadow-epitaxy of patterned superconductors on NCs, the structures reported here show promise for the realization of non-trivial topological states in multi-terminal Josephson junctions.