seems troops deployed from HQ arrive at the planet exhausted
troops deploying from headquarters
They blatantly state that the HQ is where your warlord sits while not committed to a planet, and is the area in front of the player.
To definitively answer the question in the original post:
When a player wins a battle at any other planet, his warlord (if it was at that planet) returns to its headquarters, maintaining its state. The planet remains in play, and other surviving units remain at that planet, also maintaining their state.