  The scaling of island and monomer density, capture zone distributions (CZDs),
and island size distributions (ISDs) in reversible submonolayer growth was
studied using the Clarke-Vvedensky model. An approach based on rate-equation
results for irreversible aggregation (IA) models is extended to predict several
scaling regimes in square and triangular lattices, in agreement with simulation
results. Consistently with previous works, a regime I with fractal islands is
observed at low temperatures, corresponding to IA with critical island size
i=1, and a crossover to a second regime appears as the temperature is increased
to \epsilon R^{2/3} ~ 1, where \epsilon is the single bond detachment
probability and R is the diffusion-to-deposition ratio. In the square
(triangular) lattice, a regime with scaling similar to IA with i=3 (i=2) is
observed after that crossover. In the triangular lattice, a subsequent
crossover to an IA regime with i=3 is observed, which is explained by the
recurrence properties of random walks in two dimensional lattices, which is
beyond the mean-field approaches. At high temperatures, a crossover to a fully
reversible regime is observed, characterized by a large density of small
islands, a small density of very large islands, and total island and monomer
densities increasing with temperature, in contrast to IA models. CZDs and ISDs
with Gaussian right tails appear in all regimes for R ~ 10^7 or larger,
including the fully reversible regime, where the CZDs are bimodal. This shows
that the Pimpinelli-Einstein (PE) approach for IA explains the main mechanisms
for the large islands to compete for free adatom aggregation in the reversible
model, and may be the reason for its successful application to a variety of
materials and growth conditions.
