This chapter studies technological cooperation and competition between pharmaceutical intellectual monopolies and provides evidence of their knowledge predation and intellectual rentiership. The innovation networks of Roche, Novartis, and Pfizer are proxied using information from scientific publications and patents. Network maps are constructed based on institutional co-occurrences, thus looking at the organizations co-authoring publications with big pharmaceuticals and those co-owning these intellectual monopolies’ patents between 2008 and 2017. This analysis is completed by studying the primary funding sources of chosen big pharmaceuticals publications. Regarding the chapter’s findings, each co-publications’ network map includes a cluster integrated by big pharmaceuticals, which evidences that they jointly co-produce knowledge modules. Simultaneously, to succeed in their technological competition, these maps depict that they outsource stages of their innovation networks to subordinate institutions. Overall results show that, although these subordinate institutions contribute to achieving innovations, they do not co-own the resulting patents leaving intellectual rents predominantly in the hands of big pharma. Furthermore, we find that the US National Institutes of Health, as well as other core countries’ public agencies, are main supporters of big pharmaceuticals’ research, as declared in publications’ funding sources.