A challenge for the TW-class accelerators driving Z-pinch experiments, such as Sandia National Laboratories' Z machine, is to efficiently couple power from multiple storage banks into a single multi-MA transmission line. The physical processes that lead to current loss are identified in new large-scale, multidimensional simulations of the Z machine. Kinetic models follow the range of physics occurring during a pulse, from vacuum pulse propagation to charged-particle emission and magnetically-insulated current flow to electrode plasma expansion. Simulations demonstrate that current is diverted from the load through a combination of standard transport (uninsulated charged-particle flows) and anomalous transport. Standard transport occurs in regions where the electrode current density is a few 10(4) - 10(5) A/cm(2) and current is diverted from the load via transport without magnetic insulation. In regions with electrode current density > 10(6) A/cm(2), electrode surface plasmas develop velocity-shear instabilities and a Hall-field-related transport which scales with electron density and may, therefore, lead to increased current loss.