A layer by layer deposition model based on the assumption that each layer is formed via instantaneous conversion of sites into nuclei is analysed. The statistical procedure for taking into account the overlap of growth centres at any given level is described. The equation for the current time transient due to the nth layer is written in a closed form in terms of looped integrals where the number of loops depends on n. The transient behaviour is plotted for the first four layers. It is shown that there is no undulation in the ensemble current and the current builds in magnitude with the number of layers formed.