The recently proposed partition theory (PT) (J. Phys. Chem. A 2007, 111, 2229.) is illustrated on a simple one-dimensional model of a heteronuclear diatomic molecule, 1DAB. It is shown that a sharp definition for the charge of molecular fragments emerges from PT and that the ensuing population analysis can be used to study how charge redistributes during dissociation and the implications of that redistribution for the dipole moment. Interpreting small differences between the isolated parts' ionization potentials as due to environmental inhomogeneities, we gain insight into how electron localization takes place in H-2(+) as the molecule dissociates. Furthermore, by studying the preservation of the shapes of the parts as different parameters of the model are varied, we address the issue of transferability of the parts. We find good transferability within the chemically meaningful parameter regime, raising hopes that PT will prove useful in chemical applications.