exponent, $\eta$, that characterizes the number of pinned sites. It is computed averaging over all the runs and starting with an initial condition with a single point attached to the wall. Our best estimate is $\eta =0.80(2)$ (Figure (5)). Measuring the surviving probability, and therefore the exponents $\delta$ and $\zeta'$, is a delicate technical point because it is hard to decide when the activity of a run has ceased. We have not tackled this problem here. Lastly, we obtain $\theta_h =0.34(5)$, which is again in good agreement with the value reported for our Model 1.

![ Model 2: (A) order parameter behavior, $\langle \exp(h_w-h) \rangle$, in the vicinity of the critical point $\delta v_c =0$. From the slope of the line we get $\beta_n =0.325(5)$. (B) Decay of the order parameter, $\langle \exp(h_w-h) \rangle$, at the critical point yields $\theta_n=0.215(5)$ (cf. with Figure (2). The straight line is a guide for the eye and has a slope $-0.215$.](Fig4.eps "fig:"){width="8cm"} \[sidebyside\]

![ Model 2: number of pinned sites as a function of time for an initial condition with a single point attached to the wall. A fit for late times yields $\eta=0.80(2)$. The straight line is a guide for the eye 