Jump ball to start the game. A taps it directly out of bounds. B gets the ball for the throw in. Question is , who gets the Arrow ??
Next thing. A taps ball to a teammate who never gets control but fumbles it out of bounds. B gets the throw in but who gets the Arrow ??
I have seen it called both ways. I have read where B gets the Arrow in both situations but cannot find a reference to it in a current Rule or Case book.
How do you all call this one ??

Arrow to A.
 

On the first one, A gets the arrow. You put the ball at the disposal of B after the jump, so A gets the arrow.

I'd be interested to see where you read this, because it's wrong. As listed in 4-3, the arrow is set when:
1. Player control is established (not applicable in this case)
2. The ball is at the disposal of a free thrower (ditto)
3. The ball is at the disposal of a thrower (for a throw in) following a violation or foul before a player secures control (you had violations (out-of-bounds) during the jump in both cases -- give the ball to B and the arrow to A)