Abstract: The molecular beam epitaxial growth of Si on SiC is investigated as a prototypical system for the formation of nanoclusters on semiconductor surfaces without interface intermixing effects. The investigation clearly indicates the presence of both equilibrium and non-equilibrium effects with regard to the island formation. The existence of an equilibrium wetting layer thickness dequ independent from deposition rate R and temperature T is shown from the wetting behaviour of Si on SiC(0001) associated with a change in the surface reconstruction. After 3D island formation dequ is still present between the 3D-islands, what clearly confirms that the growth mode of Si is Stranski-Krastanov. The equilibrium wetting layer thickness is well described by equilibrium theory of heteroepitaxial growth considering strain as well as interface effects. At d > dequ and conditions that are close to the equilibrium surplus Si atoms always aggregate instantly into 3D islands. Under dynamical conditions of growth far from equilibrium, the range of 2D layer-by-layer growth can be extended to an excess wetting layer thickness (dcrit - dequ). Investigation of (dcrit - dequ) as function of R and T indicated a transition from thermodynamically to kinetically controlled regimes of 2D-3D transition by a change in deposition condition. Furthermore, the 2D-3D transition initially starts with the formation a larger 2D islands and the simultaneous formation of smaller 3D islands, which likely acts as precursors for the formation and growth of larger 3D islands. For the growth of islands during further deposition surface mass transport of adatoms is rate controlling. Post-deposition annealing of the highly stressed excess wetting layer (d > dequ) gives rise to 3D island nucleation after deposition was stopped, what could be a long lasting process because adatoms stem mainly from the wetting layer decomposition.