Magnetic divertors have been proven successful in minimizing plasma/wall interactions and in leading to high-confinement regimes in tokamaks. This suggests that similar benefits may occur in a reversed-field pinch (RFP) fitted with a divertor. Previous experiments using divertors in an RFP have used a poloidal field divertor configuration such as those used in tokamaks. This study investigates another approach, a toroidal field divertor (TFD). A simple model of a poloidally symmetric TFD is presented and used in a three-dimensional magnetohydrodynamic code to study the response of the plasma to the large poloidal m = 0 perturbations caused by the divertor coils. It is found that the topology of the RFP-TFD system is much more complex than had been expected. The three-dimensional DEBS code shows that the divertor will not hinder the formation of a reversed toroidal field in the plasma, although the dynamics of its formation is altered when toroidal effects are considered. The plasma develops flows and currents in the throat of the divertor in response to the vacuumlike divertor fields. These flows and currents tend to restore the force-free character of the plasma.