In previous work, pi-electron ring currents in several fully benzenoid hydrocarbons were calculated by means of the quasi-graph-theoretical, parameter-free Huckel-London-Pople-McWeeny (HLPM) method. It was found that for fully benzenoid hydrocarbons formed from fewer than about 17 rings all ring currents in full rings are larger in intensity than the ring current in benzene, while ring currents in the empty rings are smaller than the benzene value. There was an indication that this distinction might break down when larger systems are considered. Accordingly, these studies are here extended to a selection of fully benzenoid hydrocarbons containing up to 43 rings. It is still found that all full rings in all structures bear ring currents that are greater than the ring current in benzene but, in several of the larger systems, empty rings are found to bear ring currents greater than the benzene value. In the very largest structures examined, the ring currents in some of the empty rings are greater than the currents in as many as half of the symmetrically nonequivalent full rings. Despite this, because every full ring bears a ring current of intensity greater than that of any of the empty rings that are immediately adjacent to it, all of the full rings are regions of diatropic circulation; there is also strong diamagnetic circulation around the perimeters of each of the fully benzenoid systems studied. Both of these observations, based on the topological HLPM approach, are qualitatively in agreement with the predictions of sophisticated ab initio calculations, earlier performed on some of these fully benzenoid structures by Steiner et al.