We have used Monte Carlo simulations to study the scaling relations de
scribing submonolayer nucleation N proportional to F-y/D-x theta(z) as
a function of system size L (where N is the nucleated island density,
D the diffusion coefficient, F the flux rate, a the coverage). For is
land size distributions that obey scaling, the island density N can be
easily related to the step density, S-D. A simple model of critical s
ize cluster i(c)=1 is used. For a given system size L there is a minim
um (D/F)(min) ratio where scaling breaks down with x=y=0. These consid
erations are relevant to systems with low terrace diffusion barrier or
small substrate terraces.