Northern Ireland won't join the EU. It's too small to survive alone without the massive financial transfers it gets from London. It won't be allowed to join southern Ireland either. There is no appetite among the Irish establishment or the population to take on the massive sectarian strife still rampant there. Let alone the huge welfare costs. Taking on east germany nearly bankrupted west germany, a lesson not lost on the Irish.
Northern Ireland produces virtually nothing and is a huge consumer of welfare subsidies. It is paid massive amounts of money by London just to keep the peace. The Irish have nowhere near the capital to take on those payments and the politicians in Ireland have no desire to risk their cosy arrangements by inviting in a load of reluctant protestant politicians intent on causing trouble.
Of course the british government would love to be rid of the massive drain on their finances but Ireland certainly won't be taking them on.
As for Scotland, the EU has already stated that their application (and Northern Ireland's) can only be considered when they are fully independent from the UK. As they can't support themselves without massive subsidies from London, despite their north sea oil income, that's not going to happen any time soon. The EU knows it and have no intention of adopting any more countries like Greece.
Try getting your news from outside this place now and again.
The EU’s top leaders have said they expect the UK to act on its momentous vote to leave the union “as soon as possible, however painful that process may be” and that there will be “no renegotiation”.
The presidents of the European council, commission and parliament Donald Tusk, Jean-Claude Juncker and Martin Schulz respectively and Mark Rutte, the prime minister of the Netherlands which holds the EU’s rotating presidency, said any delay to Britain’s exit would “unnecessarily prolong uncertainty”.
Article 50 will be filed by October.