We have investigated the phase transformation mechanisms and the resulting microstructures of excimer laser-induced crystallization of amorphous Si films on SiO2. It is shown that the process can be characterized into two major regimes, based on the dependence of the grain size and the melt duration as a function of the incident energy density. It is found that at the transition between the two regimes, exceedingly large grain-sized polycrystalline films can be obtained. We call this the super lateral growth phenomenon, and propose a model based on liquid-phase regrowth from the residual solid seeds when near-complete melting of the Si film occurs.