The phenomenology of the adsorption of Fe adatoms and addimers and the diffusion of Fe adatoms on an Ultrathin titanium oxide monolayer grown on the Pt(111) Surface is investigated via density functional simulations. It is found that (i) Fe atoms adsorb on 3-fold hollow sites or defective holes of the oxide slab with interaction energies ranging from 2.3 to 4.7 eV; (ii) Fe dimers adsorb with a proportional energetics and a clear preference for horizontal rather than vertical configurations; (iii) Fe atoms diffuse over the oxide surface with energy barriers ranging from similar to 0.7-1.1 eV on the compact regions to similar to 1.6-2.0 eV on the defective regions of the film. All this points to a great importance of kinetic effects in the growth of Fe clusters on this surface, much greater than in the previously investigated cases of noble or quasi-noble metals such as Au and Pd.