1.1. Two motivating models. Let S: = {Sn}n=0,1,... be a random walk, S0 = 0 and

Abstract. We consider a general model of an heterogeneous polymer chain fluctuating in the proximity of an interface between two selective solvents. The heterogeneous char-acter of the model comes from the fact that monomer units interact with the solvents and with the interface according to some charges that they carry. The charges repeat them-selves along the chain in a periodic fashion. The main question on this model is whether the polymer remains tightly close to the interface, a phenomenon called localization, or there is a marked preference for one of the two solvents yielding thus a delocalization phenomenon. We propose an approach to this model, based on renewal theory, that yields sharp esti-mates on the partition function of the model in all the regimes (localized, delocalized and critical). This in turn allows to get a very precise description of the polymer measure, both in a local sense (thermodynamic limit) and in a global sense (scaling limits). A key point, but also a byproduct, of our analysis is the closeness of the polymer measure t