Ionization near the target plate is shown to play an important role in biasing experiments. Our previous SOL model, which calculates the induced radial electric field, is found to be inadequate to treat the new divertor geometry of TdeV. When recycling is included via the measured emission near the plate, the upgraded model correctly reproduces all the observed electric currents and fields during biasing in the new divertor configuration. A simple divertor model using this calculated field has been developed to simulate the evolution of the divertor ion and neutral parameters under the action of neutralization plate biasing. Using a 1D adiabatic fluid model for the divertor ions, a 1D convective representation for the SOL neutrals and a 0D calculation for the plenum pressure, this divertor model satisfactorily simulates most of the TdeV biasing experiments at all biasing voltages and all toroidal field directions at low line-averaged densities. The weaker agreement at high densities is largely a consequence of the crudeness of the general divertor physics rather than of the deficiency of the biasing physics implemented in the model. The model is finally used to explain the polarity asymmetries observed in divertor efficiencies during biasing, and to demonstrate that no mechanism other than plate current saturation is required to interpret the saturation of toroidal rotation observed in the SOL at large biasing voltages of either polarity.