We simulate nucleation and growth processes of thin films on the basis
of the so-called rate equation approach allowing ''atoms'' to diffuse
and rearrange whereby enhancing their co-ordination number. The resul
ting percolating structures are different from those obtained by the '
'pure'' percolation model where ''atomic diffusion'' is not taken into
account. However, the fractal properties for p = p(c) are the same as
for the percolation model with the fractal dimension of d(f) = 1.896
and for random walks of d(w) = 2.87. Moreover, d(f) and d(w), are inde
pendent on the diffusion time we choose for our simulations.