According to recent progress in the finite size scaling theory of critical disordered systems, the nature of the phase transition is reflected in the distribution of pseudo-critical temperatures T_c(i,L) over the ensemble of samples (i) of size L. In this paper, we apply this analysis to the delocalization transition of an heteropolymeric chain at a selective fluid-fluid interface. The width Δ T_c(L) and the shift [T_c(∞)-T_c^av(L)] are found to decay with the same exponent L^-1/ν_R, where

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... ∼ 0.26. The distribution of pseudo-critical temperatures T_c(i,L) is clearly asymmetric, and is well fitted by a generalized Gumbel distribution of parameter m ∼ 3. We also consider the free energy distribution, which can also be fitted by a generalized Gumbel distribution with a temperature dependent parameter, of order m ∼ 0.7 in the critical region. Finally, the disorder averaged number of contacts with the interface scales at T_c like L^ρ with ρ∼ 0.26 ∼ 1/ν_R .