Understanding the atomic processes governing the formation a heteroepitaxial interface is central to predict and control the basic physical and chemical properties of a variety of hetero-structures. With this perspective, we address in this work the dynamic behavior of Ge atoms deposited on Si-surfaces by molecular dynamics simulations using enhanced bond order potentials. We demonstrate that the deposition of Ge atoms on Si surface induces the competition between several processes including adsorption, desorption, and bulk and surface diffusion involving atomic exchange, substitution, and clustering. By tracking these process, the simulations provide unprecedented insights onto the assembly of the first atomic layer of Ge on Si, the nucleation, growth, and relaxation of islands and quantum dots as well as of defect generation in the bulk.