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