We consider simple adsorption models describing two systems [H2O on Fe(001) and O2 on Pd(100)] in which c(2×2) short-range order is formed during chemisorption, and metastable saturation states result. This ordering is characterized using concepts from correlated percolation theory. Rapid increases in average domain size near saturation are associated with ‘‘ghost percolation thresholds’’ just above saturation. Generalizing these adsorption models to include an island-forming propensity, α, is shown to move the saturation state closer to c(2×2) percolation. The α→∞ behavior is elucidated by analyzing corresponding ‘‘continuum two-phase grain growth models’’ using ideas from stochastic geometry, continuum, and random lattice percolation theory.