The geometric properties of Pb-MnO2 composite electrodes are studied, and a general formula is presented for the length of the triple phase boundary (TPB) on two dimensional (2D) composite electrodes using sphere packing and cutting simulations. The difference in the geometrical properties of 2D (or compact) and 3D (or porous) electrodes is discussed. It is found that the length of the TPB is the only reasonable property of a 2D electrode that follows a 1/r particle radius relationship. Subsequently, sphere packing cuts are used to derive a statistical electrode surface that is the basis for the earlier proposed simulations of different electrochemical mechanisms. It is shown that two of the proposed mechanisms (conductivity and a two-step-two-material kinetic mechanism) can explain the current increase at Pb-MnO2 anodes compared to standard lead anodes. The results show that although MnO2 has low conductivity, when combined with Pb as the metal matrix, the behaviour of the composite is not purely ohmic but is also affected by activation overpotentials, increasing the current density close to the TPB. Current density is inversely proportional to the radius of the catalyst particles, matching with earlier experimental results. Contrary to earlier SECM experiments, mass transport of sulphuric acid is not likely to have any influence, as confirmed with simulations. A hypothetical two-step-two-material mechanism with intermediate H2O2 that reacts on both the Pb matrix and MnO2 catalyst is studied. It was found that assuming quasi-reversible generation of H2O2 followed by its chemical decomposition on MnO2, results are obtained that agree with the experiments. If the quasi-reversible formation of H2O2 occurs near the peroxide decomposition catalyst, current increases, leading to an active TPB and to the current density that scales with 1/r. It is further emphasised that both the Pb matrix and MnO2 catalyst are necessary and their optimum ratio depends on the used current density. Yet, additional experimental evidence is needed to support the postulated mechanism.