The sub-division, along various alternative discharge paths, of lightning currents produced by direct strokes to transmission towers or earth wires is determined. Theoretical solutions are further given for the tower potentials due to such strokes. The effects of varying tower-footing resistances, length of span, and number of earth wires on the magnitude and wave-shape of the currents and potentials are investigated numerically. Frequency distributions of lightning current magnitudes and of front steepnesses of the tower current are derived. Results obtained are compared with published information from field observations.