  The interfacial adsorption W at the first-order transition in two-dimensional
q-state Potts models is studied. In particular, findings of Monte Carlo
simulations and of density-matrix renormalization group calculations, at q= 16,
are consistent with the analytic result, obtained in the Hamiltonian limit at
large values of q, that W \propto t^{-1/3} on approach to the bulk critical
temperature T_c, t=|T_c-T|/T_c. In addition, the numerical findings allow to
estimate corrections to scaling. Our study supports and specifies a previous
conclusion by Bricmont and Lebowitz based on low-temperature expansions.
