Magnetohydrodynamic (MHD) computations of direct current (DC) helicity injection for tokamak-like configurations show current drive with no ‘‘loop voltage’’ in a resistive, pressureless plasma. Self-consistently induced, hollow current profiles are unstable to resistive modes that partially relax the profile through the MHD dynamo mechanism. The resulting current profiles remain quite hollow, however, and tokamaks are not generated. The current driven by the fluctuations leads to closed contours of average poloidal flux, but the 1% fluctuation level is large enough to produce a region of stochastic magnetic field. A limited Lundquist number (S) scan from 2.5×103 to 2×104 indicates that both the fluctuation level and current profile relaxation increase with S. A simple quasilinear power scaling is consistent with these results at low S and suggests that at larger S, the fluctuation level decreases.