We propose an adsorption-desorption model for a deposit growth system, in which the adsorption and desorption of particles coexist. By means of the generalized rate equation we investigate the cluster (island) size distribution in the dynamic equilibrium state. The results show that the evolution behaviour of the system depends crucially on the details of the rate kernels. The cluster size distribution can take the scale-free power-law form in some cases, while it grows exponentially with size in other cases.
