During Ar+ laser scanning at low speeds, four kinds of crystallization zone appear on a-Si:H films deposited on quartz substrates. They are microcrystalline phase zone, solid phase zone, supercooled liquid phase zone and liquid phase laser zone, grown by liquid phase transverse epitaxies. The temperature field control model of laser crystallization of hydrogenated amorphous silicon has been proposed, by which the crystallization processes and their features can be explained.