Over and back?
 

I’m trying to find in the rule and/or the case book for this reference.

A1 throws-in at endline near A’s basket. The throw-in is touched by A2 in A’s frontcourt near the division line. Touched ball goes into backcourt, and A2 retrieves, and throws to A3 in A’s front court. Violation? I’m thinking that there was no player or team control prior to ball crossing division line, therefore no violation. Correct?

Case book play 4.12.6(b)

Correct. No team control established, no violation.

Just so I'm sure
 

There is no team control established just because it deflected off of A2, correct? That directly addresses 9-9-1 where "A player shall not be the first to touch a ball after it has been in team control in the frontcourt, if he/she or a teammate last touched or was touched by the ball in the frontcourt before it went to the backcourt." Because there was no team control (yet), no backcourt?

Correct. Team control is not established by a tip or deflection. Team control is not established until player control is established.

Perhaps we should also state that player control is established when a player on the court is holding or dribbling a live ball inbounds. A tap or a deflection is not "holding or dribbling".

We could do that, I suppose. Do you want to take care of that for me?

For a modest fee. ;)