A thorough study of direct InSb nanocrystal formations on patterned InAs (111) B substrates is provided. These nanostructures are created without the use of Au catalysts or initial InAs segments. Under the growth conditions generally used for selective-area, catalyst-free epitaxy, a wide range of InSb nanocrystal morphologies are observed. This is because the low-energy InSb surfaces, studied by first-principles calculations, are the {111} facets as opposed to the {110} facets. By controlling the V/III ratio during growth, different InSb nanostructures can be achieved. Using low V/III growth conditions, In droplets start to form and InSb nucleation takes place at the droplet-semiconductor interface only, resulting in vertical, self-catalyzed InSb nanopillars.