The question about possible influence of oxide support on the structure of deposited metal slabs was discussed for a series of TiO2 (rutile), tetragonal form of ZrO2, and some forms of γ-Al2O3 oxides, all of them being frequently applied for metal deposition and СН4 oxidation. The Pd(100) or Pd(110) slab models were constructed over defective and non-defective γ-Al2O3(100), non-defective ZrO2(001), and TiO2(001) supercells within a wide range of charge transfer. The latter includes the transfer from support to Pd slab or an opposite way, i.e., the total charge of all Pd atoms of the unit cells varies from − 10.456 to 2.768 e (both charge boundaries correspond to defective γ-Al2O3 oxide models with higher Al or O surface concentrations, respectively). Quick charge relaxation to nearly zero values starting already from the second Pd layer (the next one after contacting Pd layer) was observed irrespective of the presence of any defects that can charge the metallic slab both positively or negatively. The slab geometry, i.e., Pd-Pd length, of all layers depends on the oxide type and the defect type. After partial defect passivation over defective γ-Al2O3 surface with O2 or OH groups, Pd-Pd length converges to the same length as obtained with non-defective γ-Al2O3 model. The different Pd-Pd bond lengths were obtained in the top of 4-layer Pd slabs deposited over ZrO2 and TiO2 after relaxation relative to the convergent value for the Pd over γ-Al2O3 support. It illustrates the importance of the support type for growing metal nanoparticles if the contact domain with the support is sufficiently large.