The assault and support skill lines only increase by earning AP. You can level the Alliance War skills outside of Cyrodiil by having them slotted when you earn XP (just like any other skill), but the skill lines themselves require you to advance your war rank to level up.
Hi there, can you gain experience for an assault line skill for example rapid maneuver, by having it in your skill bar during PvE back in ebonheart for example? Or can it only level up to morph in cyrodiil? Thank you!