The residence time tau of an atom in a kink site position is a characteristic property of a growing phase. For alloys kink site positions and associated residence times must be defined for the different alloy components. For instance, for an alloy AB kink site positions A* and B* must be distinguished. Each kink site atom can react either with ions of type A or B to form new kink site positions AA*, AB*, BA* or BB*. The selectivity of the kink site positions for either A or B can be expressed by residence times tau(AA), tau(AB), tau(BA) and tau(BB). Another characterization of the selectivity is possible by the application of the finite Markov chain theory. Then selectivity constants g(A) and g(B) can be defined. Assuming equilibrium between the atoms in kink site positions and the respective ions in the electrolyte, the selectivity constants represent the ratios of the respective equilibrium constants between kink site positions and electrolyte concentrations g(A) = K-AA/K-AB and g(B) = K-BB/K-BA . If the process is rate-controlled, the selectivity constants represent the ratios of the respective rate constants of deposition. The model is applied to CoNi and SnNi alloys and to bismuth telluride. A relation is derived between selectivity constants and residence times. (C) 2007 Elsevier Ltd. All rights reserved.