Poor solubility of single-walled and multiwalled carbon nanotubes (NTs) in water and organic solvents presents a considerable challenge for their purification and applications. Macromolecules can be convenient solubilizing agents for NTs and a structural element of composite materials for them. Several block copolymers with different chemical functionalities of the side groups were tested for the preparation of aqueous NT dispersions. Poly(N-cetyl-4-vinylpyridinium bromide-co-N-ethyl-4-vinylpyridinium bromide-co-4-vinylpyridine) was found to form exceptionally stable NT dispersions. It is suggested that the efficiency of macromolecular dispersion agents for NT solubilization correlates with the topological and electronic similarity of polymer-NT and NT-NT interactions in the nanotube bundles. Raman spectroscopy and atomic force and transmission electron microcopies data indicate that the polycations are wrapped around NTs forming a uniform coating 1.0-1.5 nm thick. The ability to wind around the NT originates in the hydrophobic attraction of the polymer backbone to the graphene surface and topological matching. Tetraalkylammonium functional groups in the side chains of the macromolecule create a cloud of positive charge around NTs, which makes them hydrophilic. The prepared dispersions could facilitate the processing of the nanotubes into composites with high nanotube loading for electronic materials and sensing. Positive charge on their surface is particularly important for biological and biomedical applications because it strengthens interactions with negatively charged cell membranes. A high degree of spontaneous bundle separation afforded by the polymer coating can also be beneficial for NT sorting.