Epitaxial deposition of gallium arsenide in holes etched into gallium arsenide substrates was investigated. Single crystal deposits with excellent surfaces were obtained. The effect of substrate orientation on the degree of lateral overgrowth above the substrate surface was studied. Depositions in {100} oriented substrates produce faceted deposits, whose upper surfaces are several microns above the substrate surface. Epitaxial hole deposits with surfaces level with or nearly level with the substrate surface are obtained with accurately oriented {111}‐B substrates.