This study investigates the incremental processing of restrictive object relative clauses. The anticipation of the referent of the complex DP, as contextual information is integrated during the analysis of relative clause, is particularly considered and the possibility is explored of this sort of incremental processing being reconciled with an autonomous parser. The argument is conducted two-way: (i) by characterizing the moment in time at which the information provided by the complex DP is integrated with background information, and the conditions that allow for the anticipation of the referent of a complex DP; (ii) by considering the computational advantages of an autonomous parser (vis a vis interactive models), and possible means of reconciling the experimental results obtained. As for (i), three experiments were conducted in the visual world paradigm. Sentences with a complex DP subject containing a restrictive object relative clause were presented either concomitantly to a visually supported discourse context (Experiment 1) or preceded by it (Experiment 2). The visual context was manipulated in such a way as to enable the integration of the information provided by the complex DP and the discourse context to take place at different sentence segments. The results confirmed previously reported findings suggesting that sentences are incrementally interpreted and mapped onto the external world, and that the referent of the complex DP is search for as soon as possible. Experiment 3 was intended to verify the extent to which such an anticipation would take place in temporally ambiguous sentences (complement sentences or relative clauses), presented in normal intonation and preceded by contexts that would bias for the parsing of restrictive relative clauses. Unlike previous findings, however, the biasing context did not override Minimal Attachment. As for (ii), the on-line model of sentence computation in Corrêa and Augusto (2007) and its expansion in Augusto, Corrêa and Forster (2012) were further developed. The minimalist concept phase with a partially analyzed material being transferred to the interfaces, when adapted to left-right on-line computation, enables a partially analyzed complex DP to be minimally interpreted and integrated with background information. Additionally, the pre-activation of thematic relations on the basis of discourse/contextual information was proposed as a means of accounting for the anticipation of the referent of complex DP as the subject of the relative clause is analyzed.