  A quench in an overdamped one dimensional $\phi^4$ model is studied by
analytical and numerical methods. For an infinite system or a finite system
with free boundary conditions, the density of kinks after the transition is
proportional to the eighth root of the rate of the quench. For a system with
periodic boundary conditions, it is proportional to the fourth root of the
rate. The critical exponent predicted in Zurek scenario is put in question.
