Every twelve hours the routes are decided by Canadian and British ATC (they take it in turns) These routes will be decided mainly by weather, and the flights choice of route will be decided by destination etc.
Westerly routes are numbered A, B, C, etc from north to south, and are decided by british ATC. Easterly routes are numbered Z, Y, X, etc from south to north, and are decided by Gander (Canadian) ATC.