The growth of a binary ideal solid solution crystal from its vapor in a wide range of supersaturation is simulated using the Monte Carlo simulation method. The growth rate and surface structure obtained in the present simulation show that the growth mechanism changes from the layer-by-layer growth of smooth surfaces, through multinuclear layer-by-layer growth, to normal growth of rough surfaces, with increased supersaturation. The effective distribution coefficients for bulk., terrace, step, and kink sites show not simple dependence on supersaturation. The dependence is interpreted in the relation with the growth mechanisms, by taking account of both the kink kinetics and the relaxation by direct exchange of atoms between each kind of growth site and a vapor. (C) 2007 Elsevier B.V. All rights reserved.