We have extended an earlier study, in which we characterized in detail the electrostatic potentials on the inner and outer surfaces of a group of carbon and B(x)N(x) model nanotubes, to include several additional ones with smaller diameters plus a new category, C(2x)B(x)N(x). The statistical features of the surface potentials are presented and analyzed for a total of 19 tubes as well as fullerene and a small model graphene. The potentials on the surfaces of the carbon systems are relatively weak and rather bland; they are much stronger and more variable for the B(x)N(x) and C(2x)B(x)N(x). A qualitative correlation with free energies of solvation indicates that the latter two categories should have considerably greater water solubilities. The inner surfaces are generally more positive than the corresponding outer ones, while both positive and negative potentials are strengthened by increasing curvature. The outsides of B(x)N(x) tubes have characteristic patterns of alternating positive and negative regions, while the insides are strongly positive. In the closed C(2x)B(x)N(x) systems, half of the C-C bonds are double-bond-like and have negative potentials above them; the adjacent rows of boron and nitrogens show the usual B(x)N(x) pattern. When the C(2x)B(x)N(x) tubes are open, with hydrogens at the ends, the surface potentials are dominated by the B+-H- and N(-)-H+ linkages.