The place of the Court of Justice of the European Union (CJEU) during Brexit negotiations was a highly debated one, as one of the explicit reasons invoked to leave the EU by British authorities was not to be submitted to EU law and CJEU’s rulings. The aim of this working paper is to analyse the reasons for the specific relationship model with regard to the CJEU competences that resulted from EU-UK Brexit negotiations. While the EU-UK Trade and Cooperation Agreement (TCA) excludes the jurisdiction of the CJEU in favour of a dispute settlement system more respectful of the British sovereignty, an exception is made for the situation of Northern Ireland. The paper argues that the balance between conditionality and access/participation did now allow for the application of the EEA model of voluntary submission to the CJEU: if market power Europe has explained several aspects of EU’s external relations, it is of little use in the case of the UK’s relation to the CJEU. Hence, the paper explores two other possible explanations. The first one, drawing on the disintegration literature, argues that voluntary submission is more likely to happen in a context of integration than of disintegration. In other words, when the relationship between the EU and the affiliated government unfolds in a context of disintegration, where both partners seek to keep their advantages, ad hoc arrangements outside the legal framework of the EU seem plausible. However, disintegration alone is not a sufficient framework to explain the precise situation in which the CJEU is replaced by an ad hoc litigation settlement. Negotiations took place in a context of uncertainty regarding what the precise consequences of the negotiated result might be. A context of uncertainty is particularly germane to power-politics, which can reinforce the asymmetries in patterns of complex inter-dependence. The second explanation then focuses on domestic politics as the main determinant: the EU may push in favour of voluntary submission, but this model can only be chosen if it serves the purpose of the third state’s political power and is accepted by the governed.