We consider the problem of estimating the size of a population of interest, by integrating a set of administrative sources to be used as capturing lists in a  capture-recapture setting. In this setting, we address the presence of lists which target a subset of our population by means of an inferential approach developed in the context of inference with missing data. We present the use of an extended family of latent class models which relaxes the conditional indipendence assumption, in presence of missing data.