Results from steady and unsteady, two-dimensional simulations of tertiary current distributions at and below the limiting current density are presented. The simulations are based on dilute-solution theory, with coupling of the concentrations of the ionic species through the electrical field. The electrical field is calculated from the electroneutrality constraint. Results confirm and extend previous theoretical predictions of the electrical migration enhancement of the limiting current To demonstrate the potential utility of general current-distribution solvers, measured temporal variations of the rate of copper deposition in the presence of an oscillating shear flow are measured and simulated. Experiments agree well with simulations.