Abstract <p>Laser annealing of structural steels is often used for surface hardening or coating deposition through remelting of the surface layer that leads to better microstructure parameters and mechanical properties. In this paper, an analysis of microstructure selection is performed under non-equilibrium conditions of rapid solidification. The microstructure selection map (MSM) is constructed as a function of the solidification velocity and local temperature gradient. A transition to structureless solidification is determined in the vicinity of the velocity of absolute morphological stability of the advancing front.</p>