During heteroepitaxial overlayer growth multiple crystal domains nucleated on a substrate surface compete with each other in such a manner that a domain covered by neighboring ones stops growing.The number density of active domains ρ decreases as the height h increases.A simple scaling argument leads to a scaling law of ρ~ h~(-γ) with a coarsening exponent γ=d/z,where d is the dimension of the substrate surface and z the dynamic exponent of a growth front.This scaling relation is confirmed by performing kinetic Monte Carlo simulations of the ballistic deposition model on a two-dimensional(d=2) surface,even when an isolated deposited particle diffuses on a crystal surface. During heteroepitaxial overlayer growth multiple crystal domains nucleated on a substrate surface compete with each other in such a manner that a domain covered byiates ones stops growing. The number density of active domains ρ decreases as the height h increases. A simple scaling argument leads to a scaling law of ρ ~ h ~ (-γ) with a coarsening exponent γ = d / z, where d is the dimension of the substrate surface and z the dynamic exponent of a growth front.This scaling relation is confirmed by performing kinetic Monte Carlo simulations of the ballistic deposition model on a two-dimensional (d = 2) surface, even when an isolated deposited particle diffuses on a crystal surface.