We present. first-principles results obtained within the framework of density functional theory referring to Mg adsorption and its incorporation in two distinct InN surfaces ((0 0 0 1), (0 0 0 (1) over bar)) under various adsorption coverage conditions. In all deposition cases we deducted the bonding characteristics and the electronic character of the structures. It is found that in In rich conditions N-polarity facilitates the diffusion of In and Mg adatoms while In-polarity facilitated the Mg-induced weakening of adatom (In, Mg)-surface interactions for small doses of Mg. This implies that the Mg dopant decreases In and Mg diffusion barrier leading to smoother surfaces. Interestingly, we found significant differences of Mg incorporation in In-and N-polar surfaces: Mg incorporation is easier in bare N-polar than in the In-polar surface, except when an In contracted bilayer is formed on top of the InN. In the case of In-polarity, Mg impurities start to penetrate in the subsurface region as the Mg coverage increases. In the contracted In bilayer case, Mg incorporation in the InN is significantly enhanced. Furthermore, we found that the presence of Mg close to the (0 0 0 (1) over bar) InN surface does not alter significantly the local structure, contrary to the In-polarity case in which a flattening of the bilayers is observed at the highest Mg coverage that may lead to the formation of basal inversion domain boundaries. (C) 2009 Elsevier B. V. All rights reserved.