  Ab initio calculations indicate that the ground state for Ga adsorption on Al
(100) is on-surface with local unit coverage. On Ga-coated Al (100), the bridge
diffusion barrier for Al is large, but the Al$\rightarrow$Ga {\it exchange
barrier is zero}: the ensuing incorporation of randomly deposited Al's into the
Ga overlayer realizes a percolation network, efficiently recoated by Ga atoms.
Based on calculated energetics, we predict rough surface growth at all
temperatures; modeling the growth by a random deposition model with partial
relaxation, we find a power-law divergent roughness $w\sim t^{\,0.07\pm0.02}$.
