This article completes the study of adsorption at the centers of the hexagons (hollows) making up zigzag (M, 0) singlewalled carbon nanotubes, with first- and second-neighbor adsorbate-adsorbate interactions, using our established transfer matrix method. We have previously determined that the low temperature energy phase diagrams for attractive first-neighbors are the same for all M. We now show that this is not the case for repulsive first-neighbors. Therefore, our model predicts whether first-neighbors are repulsive or attractive, based solely on whether or not experimental results are M-dependent. The numerical computations are carried out for values of M <= 18. The progressions with increasing M of the structures of the occupational configurations of the phases, and of the low temperature phase diagrams, are compared with the results known in the infinite-M limit. They strongly suggest six families of low temperature phase diagrams with M = 4, 6, 8, 10, 12, and 14, modulo 12. This can be experimentally verified, and can then he used to make further predictions on hollow adsorption on any zigzag (M, 0) nanotube.