Would there be a poll in the south or would it just happen?
Under the Good Friday Agreement, if there’s credible information that the majority of Northern Irish voters would vote to leave the UK, then the Northern Ireland Secretary of State is empowered to call a formal vote on the issue.
The rest of the United Kingdom has no input. That is, Westminster cannot, in theory, stop or postpone Northern Ireland’s vote on the matter, nor can Westminster ignore or cancel the outcome, regardless of whether it’s stay or leave. Officially. However, the Tories, who are in power now, are the Conservative and Unionist Party. Extrapolating from their response to the SNP’s calls for another independence referendum for Scotland, they and their Northern Ireland Secretary may choose to be ‘blind’ to any and all credible information that the Northern Irish people want to leave the UK. A Labour Party government, or a coalition government without the Tories, is more likely to permit a border poll, but the chances of Labour forming a government at present, either alone or in coalition, seem remote.
Similarly, under GFA, the Republic of Ireland can call a vote to decide whether or not to unite the two jurisdictions. As part of GFA, the Republic gave up its constitutional claim of jurisdiction over the island of Ireland, and officially see unification as a long term aim, subject to the wishes of the people of the island of Ireland. Again, depending on economic conditions, the Irish government might try to postpone a border poll, but, unlike the UK, none of the parties have a vested interest in preventing one taking place.
If NI voted to stay in the UK, they stay, the result of a border poll in the Republic notwithstanding. If NI voted to leave, but the Republic voted against unification… I don’t know. I don’t know if the Republic would vote against unification. However, there would be a transitional period during which Northern Ireland’s exit was thrashed out: perhaps, if the Republic did vote against unity, that period could be extended so that further talks and negotiations could take place. Northern Ireland would not be in a comfortable place during that process, though. No change there…