By studying the time-dependent axial and radial growth of InSb nanowires, we map the conditions for the synthesis of single-crystalline InSb nanocrosses by molecular beam epitaxy. Low-temperature electrical measurements of InSb nanocross 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 nanocross junction is connected by few-channel quantum point contacts in the connecting nanowire terminals, we show that transport through the junction is ballistic except close to pinch-off. Combined with a new concept for shadow-epitaxy of patterned superconductors on nanocrosses, the structures reported here show promise for the realization of non-trivial topological states in multi-terminal Josephson Junctions.