The Smoluschovski equations are applied to a growth process in which short pulses of atomic beams are deposited on a smooth surface. After each pulse the atoms are allowed to diffuse and nucleate until the monomers disappear. The normalized total density of clusters and the average cluster size are calculated as a function of the number of pulses. These magnitudes exhibit a universal behavior in the sense that they do not depend on surface diffusion but only on the cluster geometry. Properly scaled, they do not depend on the coverage achieved by each pulse. Simple approximation schemes are provided for 0D and 1D clusters.