Methods to form stable dispersions of single wall carbon nanotubes (SWNT) in aqueous medium have generally relied on classical approaches to attain kinetic stability by electrostatic and/or steric stabilization. This has been achieved in numerous ways including by the adsorption of conventional ionic or nonionic surfactants, bile salts, peptide amphiphiles, high molecular weight polymers, hydrophilic block copolymers, and also by the adsorption of block copolymer micelles. In contrast, we present an alternate approach based on self-assembly, utilizing block copolymer molecules that self-assemble to form cylindrical micelles and are also prone to self-assembly around cylindrical nanoparticles. In the polymer-nanoparticle aggregates, the nanoparticle is solubilized inside a cylindrical micelle in contrast to having the block copolymer or block copolymer micelles adsorbed on the nanoparticle. The formation of SWNT dispersions in water using such self-assembly has been investigated with a number of Pluronic triblock copolymers, selected based on their tendency to form cylindrical micelles. Further, we also manipulated the cylinder formation and properties of cylinders by the addition of cyclohexane as a solubilizate. For comparison, the dispersion of SWNTs was also achieved using the conventional surfactants sodium dodecyl sulfate and Triton X-100 and the hydrophilic Pluronic block copolymer, F98. A quantitative method to characterize the dispersion state of nanotubes was developed in terms of the "resonance ratio" and "normalized width" of a characteristic UV-vis spectral feature of the SWNT, with the existence of narrow intense peaks implying a better dispersion. Pluronic P84 with cyclohexane as solubilizate, Pluronic P103, and Pluronic P123 yielded very good dispersions. For all three systems, the dispersion stability remained unaffected when the systems were subjected to temperature perturbation. Further, for all three systems, the method of preparing the dispersion did not affect the end state of the dispersion. These suggest that the nature of stability of these dispersions is more likely to be thermodynamic rather than just kinetic.