The discharge time dependence of key parameters of electrostatic capacitors employing a dielectric composed of the oxide film formed on titanium via anodization, saturated with various aqueous ion solutions, that is tube-super dielectric materials (T-SDM), was thoroughly documented for the first time. The capacitance, dielectric constant, and energy density of novel paradigm supercapacitors (NPS) based on T-SDM saturated with various concentrations of NaNO 3 , NH 4 Cl, or KOH were all found to roll-off with decreasing discharge time in a fashion well described by simple power law relations. In contrast, power density, also well described by a simple power law, was found to increase with decreasing discharge time, in fact nearly reaching 100 W/cm 3 for both 30 wt% KOH and NaNO 3 solution-based capacitors at 0.01 s, excellent performance for pulsed power. For all capacitors, the dielectric constant was tested, which was greater than 10 5 for discharge times >0.01 s, confirming the materials are in fact T-SDM. The energy density for most of the capacitors was greater than 80 J/cm 3 of dielectric at a discharge time of 100 s, once again demonstrating that these capacitors are competitive for energy storage not only with existing commercial supercapacitors but also with the best prototype carbon-based supercapacitors.