In this paper we experimentally study the growth of self-assembled SiGe islands formed on Si(001) by exploiting the thermally activated surface diffusion of Ge atoms from a local Ge source stripe in the temperature range 600-700 °C. This new growth strategy allows us to vary continuously the Ge coverage from 8 to 0 monolayers as the distance from the source increases, and thus enables the investigation of the island growth over a wide range of dynamical regimes at the same time, providing a unique birds eye view of the factors governing the growth process and the dominant mechanism for the mass collection by a critical nucleus. Our results give experimental evidence that the nucleation process evolves within a diffusion limited regime. At a given annealing temperature, we find that the nucleation density depends only on the kinetics of the Ge surface diffusion resulting in a universal scaling distribution depending only on the Ge coverage. An analytical model is able to reproduce quantitatively the trend of the island density. Following the nucleation, the growth process appears to be driven mainly by short-range interactions between an island and the atoms diffusing within its vicinities. The islands volume distribution is, in fact, well described in the whole range of parameters by the Mulheran's capture zone model. The complex growth mechanism leads to a strong intermixing of Si and Ge within the island volume. Our growth strategy allows us to directly investigate the correlation between the Si incorporation and the Ge coverage in the same experimental conditions: higher intermixing is found for lower Ge coverage. This confirms that, besides the Ge gathering from the surface, also the Si incorporation from the substrate is driven by the diffusion kinetics, thus imposing a strict constraint on the initial Ge coverage, its diffusion properties and the final island volume.