The substrate contribution to the magnetic anisotropy energy (MAE) of supported nanostructures can be assessed by a site-selective manipulation of the spin-orbit coupling (SOC) and of the effective exchange field Bex. A systematic study of Co adatoms and Co monolayers on the (1 1 1) surfaces of Cu, Ag, Au, Pd and Pt is performed to study common trends in this class of materials. It is found that for adatoms, the influence of the substrate SOC and Bex is relatively small (10-30% of the MAE) while for monolayers, this influence can be substantial. The influence of the substrate SOC is much more important than the influence of the substrate Bex, except for highly polarizable substrates with a strong SOC (such as Pt). The substrate always promotes the tendency to an out-of-plane orientation of the easy magnetic axis for all the investigated systems.