We report on the morphology and properties of the surface formed by molecular-beam epitaxy on shallow mesa gratings on patterned GaAs(3 1 1)A and GaAs(1 0 0). On GaAs(3 1 1)A substrates, the corrugated surface formed after GaAs growth on shallow mesa gratings along [0 1 (1) over bar] is composed of monolayer high steps and (3 1 I)A terraces. These pattern induced steps which are different on opposite slopes play an important role in InAs growth on this novel template leading to distinct lateral modulation of the island distribution. On GaAs(1 0 0) substrates, growth on shallow mesa gratings along [0 1 1], [0 1 0] and [0 1 (1) over bar] is drastically sensitive to the pattern direction due to the difference of steps along [0 1 1] and [0 1 (1) over bar]. (C) 2002 Elsevier Science B.V. All rights reserved.