Numerical multidimensional simulations are presented that deal with the effect of material parameters on the current distribution in porous mixed conducting solid oxide fuel cell cathodes where the oxygen incorporation into the electrolyte takes place through the bulk of the electrode. In particular, it is demonstrated that, depending on the ratio k(q)/D-q (surface incorporation factor/diffusion coefficient of oxide ions), different regimes can be distinguished: For large k(q)/D-q values, only small regions close to the three-phase boundaries are relevant with respect to the oxygen reduction; a decreasing k(q)/D-q ratio activates an increasingly larger portion of the cathode. The impact of geometrical parameters (grain size, three-phase boundary length, surface area, etc.), and thus suggested optimum geometries, depend on k(q)/D-q. The simulations showed that either porous cathodes with high surface areas (for low k(q)/D-q) or composite cathodes (for high k(q)/D-q) are recommended to achieve low polarization resistances.