According to RTE (Ireland’s National broadcaster) the EU would want a swift divorce from the UK in the event of a Brexit and would only after that be prepared to start negotiations on a new EU/UK relationship, see link below.
Based on an assumption that the UK gives notice to leave the EU at a special summit the weekend after the referendum, RTE reports that the EU would want to start negotiations on the mechanics of the exit so that the UK would leave the EU on 1st July 2018.
The other 27 EU member states would not be prepared to extend the 2 year period to negotiate a more comprehensive exit agreement.
RTE cites two unnamed sources who confirm this.
This is in stark contrast to various Leave campaigners who assert that the EU would be falling over itself to negotiate an exit agreement favourable to the UK.