Research interest in indium antimonide (InSb) has increased significantly in recent years owing to its intrinsic properties and the consequent opportunities to implement next-generation quantum devices. Hence, the precise, reproducible control over morphology and crystalline quality becomes of paramount importance for a practical quantum-device technology. Here, we investigate the growth of InSb nanostructures with different morphologies on InAs stems without pre-growth efforts (patterning). InSb nanostructures such as nanowires (1D), nanoflags (2D) and nanocubes (3D) have been realized by means of Au-assisted chemical beam epitaxy by tailoring the growth parameters like growth temperature, precursor fluxes, sample rotation and substrate orientation. Through morphological and crystallographic characterization, all the as-grown InSb 2D nanostructures are found to be single-crystalline with zinc blende structure, free from any defects such as stacking faults and twin planes. The existence of two families of 2D nanostructures, characterised by an aperture angle at the base of 145° and 160°, is observed and modelled. This study provides useful guidelines for the controlled growth of high-quality InSb nanostructures with different shape.