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According to recent progress in the finite size scaling theory of criticaldisordered systems, the nature of the phase transition is reflected in thedistribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble ofsamples $(i)$ of size $L$. In this paper, we apply this analysis to thedelocalization transition of an heteropolymeric chain at a selectivefluid-fluid interface. The width $\Delta T_c(L)$ and the shift$[T_c(\infty)-T_c^{av}(L)]$ are found to decay with the same exponent$L^{-1/\nu_{R}}$, where $1/\nu_{R} \sim 0.26$. The distribution ofpseudo-critical temperatures $T_c(i,L)$ is clearly asymmetric, and is wellfitted by a generalized Gumbel distribution of parameter $m \sim 3$. We alsoconsider the free energy distribution, which can also be fitted by ageneralized Gumbel distribution with a temperature dependent parameter, oforder $m \sim 0.7$ in the critical region. Finally, the disorder averagednumber of contacts with the interface scales at $T_c$ like $L^{\rho}$ with$\rho \sim 0.26 \sim 1/\nu_R $.Comment: 9 pages,6 figure

Delocalization transition of the selective interface model: distribution of pseudo-critical temperatures