We study the formation of GaAs quantum dots (QDs) by droplet epitaxy on various GaAs surfaces. The fabrication process consists of two steps. First, liquid Ga droplets are grown in a Volmer-Weber-like mode. This is followed by crystallization under As pressure. We demonstrate fabrication of droplet epitaxial GaAs QDs on (0 0 1), vicinal (0 0 1), (110), and (3 1 1)A GaAs Surfaces. On (3 1 1)A GaAs, QDs are formed with higher density and smaller height compared to (0 0 1) and (1 1 0), which is attributed to a higher energy barrier for surface diffusion. Values of the surface diffusion barrier are determined and its influence on temperature-dependent QD density is studied by means of a QD growth model. On vicinal (0 0 1) surfaces, step bunches are found to act as preferred nucleation sites for GaAs QDs which opens the possibility for a lateral positioning of the QDs by pre-patterning. (C) 2008 Elsevier B.V. All rights reserved.