Epitaxial growth of the chalcopyrite-structure semiconductor Cu(In,Ga)Se2 alloys on (111)A and B, (110), and (100) GaAs was studied and a growth model is proposed. These semiconductors are prime candidates for high-efficiency thin film solar cells and have potential in thin film transistor applications. Surface morphologies result from a mixture of surface-energy and nucleation and growth dominated phenomena. Surface energy considerations drive all observed surface planes to decompose into close packed facets, some including large numbers of surface steps. Comparison of the bulk structure and morphologies of the different surfaces indicate that nucleation of surface terraces on close-packed Se-terminated planes and their growth dominates the evolution of surface morphologies. Relatively slow nucleation of terraces on metal terminated close packed planes leaves these very smooth relative to the Se-terminated faces. Structural and electronic properties measurements show that point-defect clusters occur in large numbers in this material and can spontaneously organize on specific planes. The creation of these clusters during facet growth is proposed to be responsible for the observed step motion and consequently for the surface morphologies. Results show that epitaxial temperatures vary significantly from ~700 C on the (111)B surface to ~540 C on (110). The epitaxial temperature is proposed to be related to the availability of Se- and metal-terminated surface step edges. The organization of the point defects during growth appears to lead to a physical separation between the defects responsible for p-type doping and the conduction path for holes, permitting a nearly constant 300K hole mobility of 300 cm2/V-sec over a wide range of hole concentrations.