In the Attrition Phase, do out-of-supply spaces change control, or only spaces holding units?

Question

Accepted Answer

Any space that would eliminate a friendly combat unit for lack of supply changes control, whether or not it holds units, unless it contains an undestroyed friendly fort (14.3.6). Empty Cetinje, Arabia and Libya convert the same way. Serbian spaces are the exception: they only convert when CP units enter them. Control can switch back and forth from turn to turn.

Paths of Glory

In the Attrition Phase, do out-of-supply spaces change control, or only spaces holding units?