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Many promising supercapacitor electrode materials have high resistivity and require conductive additives to function effectively. However, the detailed role of the additive is not understood. Here, this question is resolved by applying a quantitative model for resistance-limited supercapacitor electrodes to Co(OH)2-nanosheet/carbon nanotube composites. Without nanotubes, theory predicts and experiments show that while the low-rate capacitance increases linearly with electrode thickness, the high rate capacitance decreases with thickness due to slow charging. Experiments supported by theory show that nanotube addition has two effects. First, the nanotube network effectively distributes charge, increasing the intrinsic electrode performance to the limit associated with its accessible surface area. Second, at high-rate, the increased electrode conductivity shifts the rate-limiting resistance from electrode to electrolyte, thus removing the thickness-dependent capacitance falloff. Furthermore, the analysis quantifies the out-of-plane conductivity of the nanotube network, identifies the cross-over from resistance-limited to diffusion-limited behavior, and allows full electrode modeling, facilitating rational design. [ABSTRACT FROM AUTHOR]