Pressing Action

[Cyber-Ref]

Team A scores a basket, field goal or live free throw. Ball goes through ring. Team A begins to set up full court press. Team B does not immediately possess the ball.

What are Team B's responsibilities and time contraints by rule to begin inbounding in this situation?

What are the official's responsibilities (especially the old lead's) as far as assisting or not assisting Team B get play started again?

Or more to the point:

Does the referee on the inbounding baseline handle the ball?