The transport of charged particles in a high power impulse magnetron sputtering (HiPIMS) discharge is of considerable interest when optimizing this promising deposition technique with respect to deposition rate and control of the ion acceleration. In this study the internal current densities Jφ (azimuthal direction) and Jz (axial direction) have therefore been spatially and temporally resolved in the bulk plasma region above a cylindrical magnetron using Rogowski coils. From the measurements a phenomenological model has been constructed describing the evolution of the current density in this pulsed plasma. The core of the model is based on three different types of current systems, which characterize the operating transport mechanisms, such as current transport along and across magnetic field lines. There is a gradual change between these current systems during the initiation, build-up and steady state of a HiPIMS plasma. Furthermore, the data also show that there are spatial and temporal variations of the key transport parameter Jφ/Jz, governing the cross-B resistivity and also the energy of the charged particles. The previously reported faster-than-Bohm cross-B electron transport is verified here, but not for all locations. These results on the plasma dynamics are essential input when modeling the axial electric field, governing the back-attraction of ionized sputtered material, and might furthermore provide a link between the different resistivities reported in HiPIMS, pulsed-DC, and DC magnetron discharges.