The desorption kinetics of molecular beam deposited ultrathin films of CCl{sub 4} and amorphous solid water (ASW) are studied. Overlayers of ASW impede CCl{sub 4} desorption until the onset of crystallization, whereupon the CCl{sub 4} desorbs abruptly. The abrupt desorption occurs through connected pathways that are formed in the water overlayer during the nucleation and growth of crystalline ice from ASW. The onset of the abrupt desorption corresponds to the threshold for dynamic percolation. As the crystallization proceeds, the number of connected pathways rapidly increases, giving rise to the episodic release of CCl{sub 4}. {copyright} {ital 1997} {ital The American Physical Society}