GaAs was grown on patterned [100] on- and off-axis GaAs substrates by organometallic vapor-phase epitaxy (OMVPE). Patterned mesas were observed to change shape because lateral growth rates varied by more than an order of magnitude in different crystallographic directions. For this study, misoriented GaAs (100) wafers were polished 3 degrees toward the nearest [110] or [111] family of directions, and 320 nm high cross-shaped mesas were fabricated. OMVPE growth was performed between 550 degreesC and 650 degreesC for Ih at a vertical growth rate of approximately 1.3 mum/h. Atomic force microscopy showed that three effects have a powerful influence on lateral growth initiated at mesa sidewalls. First, the symmetry of the dominant surface reconstruction has a major effect on the diffusion of Ga adatoms. Rapid Ga diffusion occurs along the [011]-[0 -1 - 1] axis in OMVPE, or the perpendicular [0 - 11]-[01 - 1] axis in molecular beam epitaxy, and appears to be a result of the different surface reconstructions which exist in the two growth ambients. Second, misorientation of the wafer causes a growth asymmetry as Ga adatoms move preferentially from high-to-low terraces. When terrace steps descend toward a mesa wall, rapid lateral growth away from the wall is always observed. When terrace steps descend away from a mesa wall, little lateral growth occurs and even reduced vertical growth may be observed. When the misorientation and reconstruction symmetries align, the surface acts like an atomic diode and the rapid lateral growth can exceed the vertical growth rate by more than an order of magnitude. Third, on misoriented substrates, step bunching increases with increasing temperature, and this can lead to significant changes in the original shape of a mesa. A growth model is presented which relates the lateral growth rate in different crystallographic directions to the substrate misorientation, the growth temperature, and the partial pressure of As during growth. It is also shown that different surface reconstruction patterns are related to chemical species with continuously varying concentrations rather than thermodynamically distinct phases.