For example, in ETOPS, an aircraft over the North Atlantic loses both engines. Can the pilot immediately alter course to the nearest airfield, or must they wait for ATS authorization?
Does the aircraft have more than 2 engines? If it doesn't all bets are off and ATC will be told of the aircrews plans. If (and over the ocean thats a BIG if) ATC can assist we will ,but one of the tasks will be to give emergency traffic information to adjacent aircraft and to assist the crew as much as possible.