Sixteen mesoporous vanado-phosphoro-aluminate solids, of the general formula Al100PXVY (X, Y = 0, 5, 10, 20), have been prepared and characterized by their N-2 adsorption/desorption isotherms. The materials were truly mesoporous, and the addition of P and/or V affects in a very precise and profound way the corresponding specific surface areas SP (m(2) g(-1)), specific pore volumes (cm(3) g(-1)), the mean hydraulic pore diameter d(p) (4V(p)/S-p) (nm), the maximum of the pore size distribution (psd) d(max) (nm), and the full width at half-maximum (fwhm) (nm) of the psd. The pore connectivity c was also determined and the dimensionality D-cc of adsorption was estimated in the pressure range where capillary condensation of N-2 in the pores takes place. The dimensionality D-cc was found to be related to the d(max), reduced over the fwhm, via the relation D-cc approximate to 3.7(d(max)/fwhm). The two parameters, dimensionality D-cc and connectivity c, are also related to each other via the simple relation log proportional to -1.83 log D-cc, which in turn results in the relation log c proportional to -1.83 log(d(max)/fwhm). A parallelism is drawn between the connectivity of pores in solids and its relation to the pore size, on one hand, and the degree of branching b of trees and its relation with the branch diameter d(k), on the other. Using allometric relations already established for such hierarchically developed natural systems, that is, trees, we reach a relation between b and d(k) of the form log b proportional to -2.34 log(d(k,max)/2d(mean)) where d(k,max) is the average diameter of the higher order (thinner) branches in a typical tree and d(mean) is the arithmetic mean diameter of all branches of that tree. The reasons for these similarities are discussed.