We report a model for metalorganic vapor-phase epitaxy on non-planar substrates, specifically V-grooves and pyramidal recesses, which we apply to the growth of InGaAs nanostructures. This model-based on a set of coupled reaction-diffusion equations, one for each facet in the system-accounts for the facet-dependence of all kinetic processes (e.g., precursor decomposition, adatom diffusion, and adatom lifetimes) and has been previously applied to account for the temperature-, concentration-, and temporal-dependence of AlGaAs nanostructures on GaAs(111)B surfaces with V-grooves and pyramidal recesses. In the present study, the growth of In(0.1)2Ga(0.88)As quantum wires at the bottom of V-grooves is used to determine a set of optimized kinetic parameters. Based on these parameters, we have modeled the growth of In0.25Ga0.75As nanostructures formed in pyramidal site-controlled quantum-dot systems, successfully producing a qualitative explanation for the temperature-dependence of their optical properties, which have been reported in previous studies. Finally, we present scanning electron and cross-sectional atomic force microscopy images which show previously unreported facetting at the bottom of the pyramidal recesses that allow quantum dot formation. (C) 2015 AIP Publishing LLC.