The pseudostagnation graphs of the current density induced by a magnetic field perpendicular to the plane of the carbon atoms of benzene and cyclopropane, chosen as archetypal of pi- and alpha-aromatic molecules, have been worked out. Saddle nodes forming the saddle stagnation lines of the pseudostagnation graph have been connected by means of trajectories of the current density, which delimit the border of four different sectors of flow around each saddle line. The merging of all such boundary trajectories provides local zero-flux surfaces in the pseudocurrent density, i.e., separatrices, which split the induced current density field in a number of three-dimensional domains of flow. As a result, a new partition scheme, corresponding to the physical flow that one could observe, has been obtained. For benzene and cyclopropane, by integration of the current density over the various spatial domains, the parallel component of the nuclear magnetic shielding and magnetizability tensors has been decomposed into contributions that are hard to reconcile with any atomic models of partition.