The European Commission Task Force for the Preparation and Conduct of the Negotiations with the United Kingdom under Article 50 TEU has submitted a Position Paper on Judicial Cooperation in Civil and Commercial Matters on 28 June 2017. It claims to contain the main principles of the EU position in this regard. A closer look, however, reveals that it only deals with the temporal application of the relevant EU instruments, notably the Brussels Ia Regulation, the Rome I Regulation and the Rome II Regulation. It suggests that all EU instruments should continue to apply to all choices of forum and choices of law made prior the withdrawal date and that judicial cooperation procedures that are ongoing on the withdrawal date should continue to be governed by the relevant provisions of Union law applicable on the withdrawal date.
The Position Paper is available here.