In the same spirit as a recent periodic DFT Study on the interaction of MoS2 layers on gamma-alumina and anatase-TiO2 surfaces [C. Arrouvel et aL, J. Catal. 232 (2005) 161], the present DFT investigation brings new insights comparing the thermodynamic stability of MoS2 particles anchored by S-edge and Mo-edge on these two supports under HDS conditions. It is shown that the S-edge interacts more weakly with the gamma-alumina and anatase-TiO2 surfaces. In particular, the epitaxial relationship found for the Mo-edge is not recovered for the S-edge on anatase. The determination of adhesion energies of Mo5CoSn Clusters on the two supports shows that Co weakens the edge anchoring of the active phase. The equilibrium morphology and the edge-wetting regime of the supported MoS2 particles are deduced using the Gibbs-Curie-Wulff formalism. The DFT results combined with the morphological models of supported particles lead to a precise evaluation of the proportion of anchored and free edge sites (including the relative distribution of S-edge and Mo-edge sites). This analysis provides a new interpretation based on the edge-wetting concept of the two supports by MoS2 and CoMoS particles to explain the different HDS activities observed. (c) 2006 Elsevier Inc. All rights reserved.