The phenomenon of percolative charge transport on an electrified surface during adsorption of an electrically conducting phase on a dielectric substrate has been considered for the first time. The influence of the adsorption kinetics and nucleation on the formation of percolation clusters ensuring a decrease of the charge with its subsequent neutralization has been studied. It has been established that percolation transitions play a determining role in the stability of an electric charge accumulated on a dielectric surface. An increase in the rate of spontaneous nucleation and initial surface coverage with an electrically conducting phase leads to a decrease in the duration of the percolation transition.