A no deal scenario is by no means a legal or economic vacuum.

After the UK leaves as seems increasingly likely it will be in a similar relationship with the EU as is any country outside of the EU (referred to in the EU Treaties as 'third States' or 'third countries'). 

This research addresses some legal aspects of the Brexit process as it enters the final six months before the deadline for withdrawal.

The EU is an international organisation (although it is much closer to being like a State than other international organisations in terms of the range of EU competences and powers), with legal personality so that it can make treaties and send and receive ambassadors. The EU accepts ambassadors from third States and sends EU ambassadors to them. All EU Member States already send ambassadors to the EU, so the UK ambassador to the EU can simply continue carrying out his or her functions after Brexit, but now as the ambassador of a third State instead of as a Member State of the EU.

The EU has entered into a range of agreements with third countries about trading arrangements with those countries. A high-profile example is the treaty between Canada and the UK, the Comprehensive Economic and Trade Agreement (CETA), which has been concluded recently and is due to be fully ratified shortly. This has been proposed as a possible model for EU-UK relations after Brexit, including as the basis for the EU-UK withdrawal agreement. CETA is not as comprehensive as the EU Treaties themselves, naturally, but it is the most comprehensive of the EU free trade agreements and it should provide a ready basis for EU-UK relations after Brexit with adjustments to reflect that the UK already has a very high degree of alignment with the EU. The term 'Canada+' is quite apt to describe what is legally and economically feasible.

Brexit and to permit current arrangements to continue more or less even without a binding legal framework until a more settled policy is reached that could go further than the WTO minimum both the UK and EU will be bound to accept in any case. So a no deal scenario is by no means a legal or economic vacuum.

After the UK leaves, the relationship of the UK with the EU will be based on international law, as opposed to the 'special' rules of EU law. Thus, in the absence of an agreement under Article 50 TEU, the relationship between the EU and UK concerning trade in goods and services will be based on the law of the World Trade Organisation (WTO), of which both the UK and EU are members as contracting States. 

The 'problem' with the Irish border is easily fixable. It is not necessary to have customs checks at the Irish border if a modern customs infrastructure is implemented as has already been done in the form of TIR carnets to enable customs transit. A Canada-style CETA between the EU and UK deal will not impact on the Irish border question in a negative way, it will actually minimise customs issues since CETA involves the almost complete abolition of customs duties between Canada and the EU.