The third-rank hypermagnetizabilities of three small molecules have been evaluated at the Hartree-Fock level of accuracy within the conventional common-origin approach as well as alternative procedures formally based on continuous transformation of the origin of the electronic current density induced by a perturbing electromagnetic field. Gaugeless basis sets of increasing size and flexibility have been employed in a numerical test (i) to assess the practicality of distributed origin methods whereby the diamagnetic contribution to the current density is formally annihilated, and (ii) to estimate the degree of convergence of diamagnetic and paramagnetic contributions to tensor components. It is shown that two nice features characterize the computational scheme adopted in this study: (i) the results depend only linearly on a shift of origin; (ii) a permutational symmetry condition of tensor indices yields a natural criterion for the near-Hartree-Fock quality of computed values.