Platinum columnar growth was found on anode and cathode catalysts after 6 months of operation in hydrogen/oxygen cells (1 A cm−2) from original smooth microspheres layers with loads ca. 1 mg cm−2. The application of symmetric and asymmetric large frequency square wave potential programs in strong sulphuric acid solutions for catalyst preparation showed those effects. For columnar electrodes, current and potential distributions are not those expected for smooth surfaces and constitute the main reason of a mismatching between theory and experimental data. The employ of exact analytical solutions arising from mass/charge balances are a better way to envisage electrochemical profiles instead of numerical solutions. Columnar catalysts can be parameterized by a trochoid curvilinear profile knowing the radius and pass (from ex situ STM images) rendering values ca. ½ for both parameters. Polarization and power density curves were also mimicked from the obtained current and cell potential distributions for the rough columnar surfaces. Finally, Wagner, Damkoehler and Graetz numbers that typify the electrochemical reactor were developed applying these parametric equations using local variations of tangential and normal velocities, from which a general dimensionless equation was obtained.