Previous studies of the Hfickel-London-Pople-McWeeny (HLPM) ring-currents and bond-currents associated with the neutral and the dianionic altans, and iterated altans, of corannulene and coronene, are here extended to the hexaanions of (altan)"-corannulene and (altan)"-coronene, with n = 1, 2, and 3. The magnetic properties of some of these species were originally studied by Monaco and Zanasi using the ipso-centric approach, which is ab initio in nature. The "topological" HLPM method, by contrast, constitutes a parameter-free, quasi graph-theoretical model requiring knowledge only of the molecular graph of the conjugated system being considered and the areas assumed for its constituent rings. The HLPM calculations are partially presented by means of a novel illustrative device that we call "difference diagrams". One aim of this work is to compare predictions of this very rudimentary HLPM formalism with those of the much more sophisticated ipso-centric ab initio approach when they are both applied to the calculation of ring-current properties in this family of neutral and anionic (especially, hexaanionic) conjugated systems. For those altans and iterated altans for which ab initio calculations are available for comparison, encouraging qualitative, and even quantitative, agreement is found between the predictions of the ab initio and HLPM approaches. Other structures for which HLPM calculations are reported here but which have not yet been studied by ab initio means are offered with some confidence for possible subsequent evaluation using the ipso-centric (or any other ab initio) formalism.