Calculations of the pi current density for polycyclic aromatic hydrocarbons placed in a uniform magnetic field reveal in some cases a substantial localization on subunits. This localization can be anticipated either for molecules with a factorizable Kekule count K, in light of some theoretical models of ring currents, or for system with proper symmetry, in light of magnetic group theory. We have addressed the problem of whether the localization is compatible with a description of the current density field as a sum of current density fields, studying the sum of two purely rotational fields. When this general model is specialized with the parameters taken from benzene ring current, it turns out that two corotating purely rotational fields separated by a distance comparable to a chemical bond must be separated by a saddle point. We have looked for the occurrence of this criterion in K-factorizable molecules, chosen according to a novel corollary to Kasteleyn's theorem, in coronenes, which have patterns localized by symmetry and in some further systems reported in literature. For those systems already described to have an additive current density pattern, the separating bonds do host saddle points, which are thus effective signatures of additivity.