Low-dimensional high-quality InSb materials are promising candidates for next-generation quantum devices due to the high carrier mobility, low effective mass, and large g-factor of the heavy element compound InSb. Various quantum phenomena are demonstrated in InSb 2D electron gases and nanowires. A combination of the best features of these two systems (pristine nanoscale and flexible design) is desirable to realize, e.g., the multiterminal topological Josephson device. Here, controlled growth of 2D nanostructures, nanoflakes, on an InSb platform is demonstrated. An assembly of nanoflakes with various dimensions and morphologies, thinner than the Bohr radius of InSb, are fabricated. Importantly, the growth of either nanowires or nanoflakes can be enforced experimentally by setting growth and substrate design parameters properly. Hall bar measurements on the nanostructures yield mobilities up to ≈20 000 cm 2 V −1 s −1 and detect quantum Hall plateaus. This allows to see the system as a viable nanoscale 2D platform for future quantum devices.