The process comprises at least a first phase for separating a plurality of particles of molten steel from a bath of molten steel, a second phase for subjecting these particles, while still in the fluid state, to a first system of forces acting on the outer surface of each of the said particles and to a second system of forces acting on each element of the body of each particle, the said two systems of forces being chosen in such a way that these forces tend to impart a substantially spherical form to each of the said particles, and a third phase for removing heat from the said particles sufficient to bring them substantially to the solid state.