How is North Atlantic Deep water formed?

This is what i know please let me know if its right - it is formed in the Norwegian and Greenland Seas. The bottom topography of the entrance to these from the Atlantic has relatively shallow plateau between Scotland and Greenland and inhibits entrance of colder deeper waters from Canadian and Eurasian basins. This surface water is North Atlantic Drift (the downstream continuation of the Gulf Stream) so is relatively warm and saline for these latitudes. The shallow waters cool and therefore convect due to increases density and destabilisation of the themocline. The now deep water mixes with the highly sailine Arctic sea water (sailine from Ince formation) and then intermittedly overspills via the Denmark Strait to form NADW? Is this it? I am confuesed about the processes the NAD water undergoes in these seas - it seems a little vuage. Thanks.