In this paper we report a study that correlates the properties of superconducting MgB2 thin films with molecular-beam-epitaxy deposition parameters. We show the utility of using a thermochemical analysis of MgB2 synthesis to predict optimal growth conditions. The growth of stoichiometric films with improved crystalline quality can be achieved at enhanced temperatures using high reactant fluxes. High B flux enhances the sticking coefficient of Mg and facilitates higher growth temperatures and improved structural and electrical properties. With a Mg flux of similar to16 Angstrom/s and a substrate temperature of 300 degreesC, a superconducting transition temperature (T-c) of 37.7 K with a narrow transition width (DeltaT(c) < 1K) was observed. Our work shows that a growth model must include the strong dependence of the Mg sticking coefficient on B flux. (C) 2004 Published by Elsevier B.V.