Yes, just you on the Esper on the battlefield, until it either: Runs out of time with the time limit, dies, or uses it's overdrive when the conditions are met. You'll want to make a decision on who you give it to soon, the boss you fight soon after you recieve it was quite... hard, but no rush, and remember give it to you think deserves it most. ^^
EDIT: I personally give it to Ashe because she was crap, but now she's my best character.
EDIT: I personally give it to Ashe because she was crap, but now she's my best character.