Transport phenomena through the hollow conduits of carbon nanotubes (CNTs) are subjects of intense theoretical and experimental research. We have studied molecular transport over the large spectrum of ionic diffusion to pressure-driven gaseous and liquid flow. Plasma oxidation during the fabrication of the membrane introduces carboxylic acid groups at the CNT entrance, which provides electrostatic "gatekeeper" effects on ionic transport. Diffusive transport of ions of different charge and size through the core of the CNT is close to bulk diffusion expectations and allows estimation of the number of open pores or porosity of the membrane. Flux of gases such as N(2), CO(2), Ar, H(2), and CH(4) scaled inversely with their molecular weight by an exponent of 0.4, close to expected kinetic theory velocity expectations. However, the magnitude of the fluxes was ∼15- to 30-fold higher than predicted from Knudsen diffusion kinetics and consistent with specular momentum reflection inside smooth pores. Polar liquids such as water, ethanol, and isopropyl alcohol and nonpolar liquids such as hexane and decane were dramatically enhanced, with water flow over 4 orders of magnitude larger than "no-slip" hydrodynamic flow predictions. As direct experimental proof for the mechanism of near perfect slip conditions within CNT cores, a stepwise hydrophilic functionalization of CNT membranes from as-produced, tip-functionalized, and core-functionalized was performed. Pressure-driven water flow through the membrane was reduced from 5 × 10(4) to 2 × 10(2) to less than a factor of 5 enhancement over conventional Newtonian flow, while retaining nearly the same pore area.