Dendrite growth of metal patches on colloidal particles shows a variety of structures depending on the preparation conditions. The morphology of these patches suggests a cross-over from a reaction to a diffusion limited growth, implicating diffusion on the particle surface. Interestingly, the morphological and optical characteristics of the patches continuously change between two limiting behaviors. To understand this growth process, extensive simulations are performed, studying the fractal dimension and the dynamics of growth of a patch on a particle of a finite size, as a function of the initial density and the binding affinity of diffusing tracers. Several important growth regimes are characterized that enable to optimize the pathway for the synthesis of optically active, patchy particles.