Pulsed laser annealing of silicon implanted by Group (III, V) dopants leads to the formation of supersaturated alloys by nonequilibrium processes occurring in the interfacial region during liquid phase epitaxial regrowth. The distribution coefficient from the melt (k') and the maximum dopant substitutional solubility (CS
max) are far greater than equilibrium values and both are functions of growth velocity. Substitutional solubility is limited by lattice strain and by constitutional supercooling at the interface during regrowth. Values for CS
max obtained at different growth velocities are compared with predictions of thermodynamic limits for solute trapping.