In reply to galpinos:
As Harry says, the Gulf Stream is part of the system. Oceanographically, the Gulf Stream is the western part of the North Atlantic subtropical gyre. It starts at southern tip of Florida where waters coming from the Gulf of Mexico meet waters coming from the Atlantic North Equatorial Current. The Gulf Stream then travels north along the east coast of the USA then separates from the coast at Cape Hatteras. It continues northeasterly, meandering and shedding eddies, until it splits southeast of the Grand Banks of Newfoundland. This is the formal end of the Gulf Stream.
The southern branch carries on eastward and then southward to become the broader, slower Azores and Canaries currents and recirculating round to the North Equatorial Current. This circulation of the North Atlantic subtropical gyre is wind driven - easterly trade winds north of the equator and westerly winds at mid-latitudes.
The northern branch from the split off the Grand Banks is called the North Atlantic Current and is the current that wanders over to the UK then up between Scotland and Iceland to the coast of Norway and into the Arctic Ocean. A branch - the Irminger Current - goes up to Iceland and then over to Greenland and some of the North Atlantic Current circulates north of Iceland and ends up coming south along the east coast of Greenland.
Off Greenland there are two areas of convection where waters cool enough to sink. In the Labrador Sea - between southern Greenland and Labrador - is a gyre where water sinks to become the Labrador Intermediate water. East of northern Greenland, the cold waters sink deeper and become North Atlantic Deep Water. It is these two areas that draw the North Atlantic Current and so, should convection cease, because the water is either not cold enough or is too fresh, it is the North Atlantic Current that would be most affected and could possibly shut down. I don't really have any idea of the likelihood of that happening though.
I accept that the Gulf Stream is often used to describe the current system from Florida to the UK and further north. The above is for anyone who would like to know a little more detail about the system. I'm hoping it hasn't dated too much in the 25 years since I studied North Atlantic circulation.
I do love a good ocean current, they are fascinating.
Post edited at 17:04