I have no idea about other carriers, but I do know that when travelling from N.I or anywhere in the UK, you are supposed to provide the UK Border agency with API.
I don't like it one little bit, but there it is.
Here's an excerpt from Wiki that explains it:
In July 2008, the UK Border Agency published a consultation paper on the Common Travel Area that envisaged the imposition of identity and immigration controls on all air and sea crossings between the island of Ireland and Great Britain. Being part of the proposed electronic borders system, these controls would be accompanied by an Advance Passenger Information System on all flights and sea journeys between the islands of Ireland and Great Britain.
While passport controls were planned to be brought in between the United Kingdom and Ireland, the nature of possible identity controls between Great Britain on the one hand, and the Isle of Man, the Channel Islands, and Northern Ireland on the other, is not altogether clear. The last of these is the most controversial as Northern Ireland is a constituent part of the United Kingdom, with a prominent Ulster Unionist describing the proposed arrangements as "intolerable and preposterous". The nature of identity checks between Northern Ireland and Great Britain was characterised by the British government as follows:
"Section 14 of the Police and Justice Act 2006 introduced a new power that will allow the police to capture passenger, crew and service information on air and sea journeys within the United Kingdom. ... It is expected that this police power will only apply to air and sea routes between Great Britain and Northern Ireland. Passengers will not be required to use passports, but may be required to produce one of several types of documentation, including passports, when travelling, to enable the carrier to the meet the requirements of a police request."
As far as the land border is concerned, the UK Border Agency indicated that the border would be "lightly controlled" and a joint statement in 2008 by both governments confirmed that there are no plans for fixed controls on either side of the border