The title of the latest government position paper is a bit of a mouthful. Importantly, it deals specifically with civil, not criminal law, so it does not touch on the contentious issue of the European Arrest Warrant.
The paper confirms that we will leave the jurisdiction of the European Court of Justice, on the basis that its jurisdiction over the UK will terminate because the EU treaties will cease to apply.
This makes perfect sense as far as internal legal issues are concerned, but what of disputes which cross national boundaries? A consumer resident in the UK may wish to take a German company to court. Actually, at the moment, even with the UK still a member of the EU, Our courts are already used for 40% of global commercial arbitrations, often involving companies from countries outside the EU.
The paper does not go into detail as to how judicial cooperation will be maintained between the EU and a newly-independent UK, it merely states the benefit of maintaining such cooperation. It does list a number of international agreements on civil judicial cooperation to which the UK is a signatory, no doubt in the hope that these international agreements will smooth the way for ongoing cooperation after Brexit. It does suggest, however, than an interim period may be necessary before the final model (whatever this might be) comes into operation.
As with the previous position papers, the objectives are set forth in a reasonably straightforward way, but little is given away about the means by which they can be achieved.