What Irish Republicans want to see: a republic covering the whole island of Ireland, uniting the 26 counties of the current Republic of Ireland with the six counties of Northern Ireland.
The IRA and related groups believe in pursuing this aim by any means necessary. However, most factions of the IRA, principally the Provisional IRA have called a ceasefire and declared their intention to henceforth pursue this aim peacefully.
One Sinn Féin member once slipped up by stating publically that "we will not settle for anything less than a 36 County Republic!" The 32 County aim is ambitious enough, without adding four non-existent counties.