We perform a theoretical study of the fractal growing process on surface by using thedeposition, diffusion, aggregation method. We present a detailed analysis of the post-growth processes occurring in a nanofractal on surface. For this study we developed a method which describes the internal dynamics of particles in a fractal and accounts for their diffusion and detachment. We demonstrate that these kinetic processes are responsible for the formation of the final shape of the islands on surface after the post-growth relaxation.