The nonlinear evolution of transient electrical discharges initiated from a small charge spot on dielectric surfaces is analyzed with a transmission line model. The relation between the resistance per unit length,Rˆ, and the current,I, is assumed to be given by a local Arc Welder’s Ansatz:Rˆ‖I‖=E*, whereE* is a positive constant. Comparison is made with a similar study of discharges initiated from a large charge spot. While both studies predict conditions under which charge is, or is not, transported to a dielectric edge, significant differences in the two cases are revealed. For example, if charge is not transported to an edge, current reversal is possible if the charge spot is small, but can only be unidirectional if the spot is large.