The heterogeneous (catalytic) and the hetero-/homogeneous (catalytic and gas-phase) combustion processes of solid oxide fuel cell (SOFC) off-gases with compositions typical of a high cell utilization rate are investigated with high-fidelity 2D simulations in a platinum-coated planar channel using detailed hetero-/homogeneous chemistry. The pressures are 1-8 bar; the reactant streams have volumetric H2 and CO contents 0.7-1.5 and 5.3-9.7%, respectively; H2O and CO2 dilutions are ∼40 and ∼50%, respectively; and the global fuel/air equivalence ratio is 0.90. Water inhibits chemically the catalytic oxidation of H2, as it leads to high H(s) surface coverage that favors the recombinative desorption of H(s) to H2. On the other hand, H2O promotes chemically the catalytic oxidation of CO by creating high OH(s) coverage that in turn accelerates the CO consumption. Strong flames are established at the highest H2 content cases and for pressures p ≥ 3 bar. For all cases with vigorous homogeneous combustion, the catalytic and gas-phase reaction pathways coexist and compete with each other for the consumption of H2 and CO. The large H2O content leads to gas-phase production of H2 via the reaction H2O + H = H2 + OH. However, the gas-phase produced H2 is subsequently consumed by the catalytic pathway, such that nearly complete H2 conversion is attained at the reactor outlet. Gaseous chemistry does not affect the reactor lengths required for complete H2 conversion but substantially reduces the corresponding lengths for CO conversion. The H2 emissions decrease with increasing pressure and are in the range 8-110 ppmv, while the CO emissions increase with rising pressure and span the range 0.3-52 ppmv, thus leading to corrected CO emissions (at 15% O2) of less than 15 ppmv. Finally, the peak wall temperatures are largely acceptable in terms of catalyst thermal stability.