Highly dispersed Pt particles on γ-Al2O3 are known to catalyze dehydrogenation and hydrogenolysis of alkanes under H2 pressure which are of main concerns within the context of reforming catalysts. We first highlight recent progresses on the density functional theory (DFT) simulations of γ-Al2O3 surfaces, a prerequisite step, and then address the challenging question of γ-Al2O3-supported Pt clusters in reactive conditions. For that purpose, we report a DFT study of the thermodynamic stability of CxHy (with x = 1, 2 and 0 ⩽ y ⩽ 5) species formed upon dissociative adsorption of ethane on Pt13/γ-Al2O3 models at variable H coverages. The impact of the pressure ratio J = P(H2)/P(C2H6) is thus quantified and rationalized as a competition between CxHy and H species for cluster sites, combined with cluster morphology effects (reconstruction at high H coverage). We finally discuss these results in detail with the experimental literature.