Different exhaustive and fuzzy partitions of the molecular electron density (rho) into atomic densities (rho(A)) are used to compute the atomic charges (Q(A)) of a representative set of molecules. The Q(A)'s derived from a direct integration of rho(A) are compared to those obtained from integrating the deformation density rho(def) = rho - rho(0) within each atomic domain. Our analysis shows that the latter methods tend to give Q(A)'s similar to those of the (arbitrary) reference atomic densities rho(A)(0) used in the definition of the promolecular density, rho(0) = SigmaArho(A)(0). Moreover, we show that the basis set independence of these charges is a sign not of their intrinsic quality, as commonly stated, but of the practical insensitivity on the basis set of the atomic domains that are employed in this type of methods.