Ireland is an independant Republic.

Six counties of the Province of Ulster remain part of the United Kingdom of Great Britain and Northern Ireland (the other three counties of Ulster are part of the Republic). At the moment the six counties are mostly administrated by the Northern Ireland Assembly. Power is devolved to this body. A step toward independance (of a sort) while leaving the Union intact.

The majority of residents of Northern Ireland are pro-Union (they would like to stay part of the UK) the minority are Nationalist (they would like to see sovereignty over the six counties pass to the Republic of Ireland. I would not go so far as to say the "the people would OVERWHEALMINGLY vote to remain part of the UK" (as pierre66 seems to think) but certainly were it put to a vote tomorrow the Union would almost certainly not be dissolved.

Sorry - I just felt the need to clear that one up.