In previous studies, the Hückel-London-Pople-McWeeny (HLPM) method was used to calculate the "topological" ring currents and bond currents that are associated with the mono-altans, and the doubly and triply iterated altans, of corannulene and coronene and their respective dianions. This gave rise to some intriguing patterns in these currents, which were partially rationalized by a detailed examination of the lone nonbonding orbitals that each of these structures possesses. In the present work, the same HLPM approach is used to investigate whether analogous changes in bond-current patterns are observed when going from the neutral species to the dianions of the iterated altans derived from some other, simpler, "parents" having molecular graphs with a nullity of zero. The altans and iterated altans of three of the simplest parents are studied: the neutral species (altan)n-benzene, (altan)n-naphthalene, and (altan)n-azulene, with n = 1, 2, and 3, together with their corresponding dianions. Analogous bond-current patterns are indeed encountered, some of which are likewise rationalized by a detailed consideration of the nonbonding orbitals.