Industrial catalysts, consisting of metal species dispersed on a porous surface, are typically prepared by hydrogen treatment at high temperatures, and the migration of hydrogen constitutes the key elementary reaction that mediates the metal-support interactions and the generation of active catalytic sites. A detailed modeling of these processes is challenging especially for systems involving disordered surfaces. A debated issue is the role of the support "reducibility" on the mechanism of H-spillover processes. Transition-metal oxides such as titania significantly improve the activity and selectivity of catalysts supported on "non-reducible" oxides, such as silica, particularly in hydrogenation and dehydrogenation processes. To gain insight into the mechanism of H-migration in disordered catalysts and nano-particles, a comprehensive DFT-analysis of the potential energy surfaces is carried out for the transfer of H-atoms from a palladium-tetramer catalyst to a silica-support, represented by a substituted siloxane ring, doped with "reducible" titania. The H-migration to non-stoichiometric supports occurs via both a direct and H (2) -assisted transfer of H-atoms when the metal-catalyst is anchored to the non-bonding oxygen atoms of the support (defect sites). The calculations revealed that the transfer to different types of supports proceeds through identical pathways but significantly different barriers. The titania-promotion, as well as the addition of dihydrogen ligands to the catalyst, decreases the direct and H (2) -assisted H-migration barriers. Due to the extended transition state structures, the H-2-assisted mechanism provides access to more distant and hindered active centers, and thus can account for the "bottleneck" particle-to-particle (along grain boundaries) transport of hydrogen atoms. The H-migration to titania-promoted stoichiometric (defect-free) supports generates intermetallic Pd-Ti bonds, in contrast to the pristine silica-based catalysts, which do not form analogous bonds between palladium and silicon centers of the support. [GRAPHICS]