In order to directly control the size and in particular the position ofnanostructures naturally formed on high-index semiconductor surfaces during molecular beam epitaxy (MBE) and metalorganic vapor phase epitaxy (MOVPE), the growth on patterned high-index GaAs substrates is investigated. During MBE of (AlGa)As on patterned GaAs (311)A substrates, a new phenomenon in the selectivity of growth has been found to form a fast growing sidewall on one side of mesa stripes oriented along the [01-1] direction. Preferential migration of Ga adatoms from the mesa top as we[l as the mesa bottom toward the sidewall develops a smooth convex curved surface profile without facets. This unique growth mode that does not occur for the perpendicular stripe orientation nor on other patterned GaAs (nl 1)A and B substrates is stable for step heights down to thc quantum size regime to produce lateral quantum wires on patterned GaAs (311)A substrates. Quantum confinement of excitons in the wires has been demonstrated by the transition from twodimensional to magnetic confinement with increasing magnetic field. For device applications it is important that the wires can be stacked in the growth direction without any increase in interface roughness or wire size fluctuations, indicating a self-limiting lateral growth mechanism. Finally, in strained layer epitaxy, (lnGa)As islands can be selectively placed on the mesa top and bottom leaving entirely free the curved part along the fast growing sidewall. @: 1997 Elsevier Science Ltd.