  In this paper we study the following parabolic system
  \begin{equation*}
  \Delta \u -\partial_t \u =|\u|^{q-1}\u\,\chi_{\{ |\u|>0 \}}, \qquad \u =
(u^1, \cdots , u^m) \ ,
  \end{equation*}
  with free boundary $\partial \{|\u | >0\}$.
  For $0\leq q<1$, 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 $C^{1, \alpha}$ in space directions and half-Lipschitz in the time
direction.
