An analysis is presented of self-field accelerated quasi-one-dimensional plasma flows with zero axial current. When magnetic convection dominates over magnetic diffusion (large magnetic Reynolds number Rm\ inlet and exit current concentration layers occur, which are analyzed by asymptotic methods to zeroth order in l/Rm. Sonic passage is found in the inlet layer, which largely determines injector conditions. Near magnetosonic conditions prevail at throats or constant-area sections. Performance factors accounting for inlet convergence and nozzle divergence are derived by exploiting the smallness of pressure forces. The effect of finite magnetic Reynolds numbers is seen to be moderate down to Rm 3 for contoured channels, but to Rm s 10 for constant-area channels. Contouring is shown to be effective for control of current and dissipation concentrations.