The European Union (EU) has experienced over time substantial changes in the number and kind of actors participating in the policy process. And their relationships have evolved. But how did these changes occur exactly, and what explains this evolution? We develop and train a natural language processing (NLP) model for joint named-entity recognition and relation extraction, and apply it to the full corpus of EU legislative acts. The model identifies EU-level and national institutions as they appear in EU law, and classifies them in pre-defined categories: EU legislative institutions (Council and Parliament), the European Commission, European agencies, member states, and national competent authorities. Moreover, the model is trained to extract the semantic relations between the identified entities. By leveraging on NLP tools such as part-of-speech taggers and dependency parsers, the model identifies the instances where EU-level and national institutions are involved in either empowering or constraining relations. The model is run on a corpus of about 13,000 Council and, when involved, Parliament directives and regulations adopted between 1958 and 2019, and available from the EurLEX dataset. We employ theories of policy design to develop and test a set of expectations about the determinants of these patterns. The article addresses particularly the less investigated relations between, on the one side, EU legislative institutions and, on the other, European agencies and national competent authorities, as well as those among supranational and national administrative institutions, such as European agencies and their national counterparts.