We present a theoretical analysis of the post-growth processes occurring in nanofractals grown on a surface. For this study we have developed a method that accounts for the internal dynamics of particles in a fractal. We demonstrate that the detachment of particles from the fractal and their diffusion within the fractal and over the surface determines the shape of the islands remaining on a surface after the fractal fragmentation. We consider different scenarios of fractal post-growth relaxation and analyze the time evolution of the island's morphology. The results of our calculations are compared with available experimental observations, and experiments in which the post-growth relaxation of deposited nanostructures can be tested are suggested.