Use 'engross' when something fully captures someone's attention, not just a part of it. The magician's performance was so engaging that the entire audience was engrossed.
Pro Tip 2/3
Deep Involvement
'Engross' often signals deep mental involvement in the activity. She was engrossed in her research, forgetting about the time.
Pro Tip 3/3
Temporal Aspect
Using 'engross' usually implies the state is temporary and related to a specific activity. He was engrossed in solving the puzzle all morning.