Structural characteristics of perhydrogenated single-walled group 13 nitride, phosphide, and arsenide nanotubes have been determined by quantum chemical calculations. Partial endo-hydrogenation is energetically beneficial for nanotubes beyond 1 nm in diameter, until which full exo-hydrogenation is relevant. The molecular structures of the partially endo-hydrogenated nanotubes are derived by rolling perhydrogenated group 13-15 monolayer sheets into cylinders. The structural principles of the resulting nanotubes are strongly influenced by electrostatic interactions between polarized surface hydrogen species. Generally, a low degree of polarization results in the preference for structures analogous to the (111) sheet of the diamond-like crystal, with a high degree of polarization resulting in the preference for the corresponding (110) structures.