In this paper we study the following parabolic system Delta u - partial derivative(t)u = vertical bar u vertical bar(q-1) u chi({vertical bar u vertical bar > 0}), = (u(1), ... , u(m)), with free boundary partial derivative{vertical bar u vertical bar > 0). For 0 <= q < 1, we prove optimal growth rate for solutions u to the above system near free boundary points, and show that in a uniform neighbourhood of any a priori well-behaved free boundary point the free boundary is C-1,C-alpha in space directions and half-Lipschitz in the time direction.