A systematic study on the Si dot formation after chemical vapor deposition on silicon oxide substrates is presented. The process has been followed from the early stages of the dot formation up to 25% of coverages. Structural characterization has been performed by means of energy filtered transmission electron microscopy, which allowed us to observe dot sizes down to 0.5 nm in radius. The nanodots are shown to be surrounded by a depleted zone, where no new Si dots are observed to nucleate. This has been attributed to the adatoms capture mechanism by pre-existing dots, during the deposition. The dot radius and the capture size are shown to collapse onto the same curve, thus indicating the scaling behavior of the process. The adatom diffusion process is shown to restrict the number of nucleation sites, the final dot size and the dot position, thus driving the process toward partial self-order.