This has probably been asked a hundred times before, but ....

A1 throws A2 a pass as A2 is running up the court. A2 cannot get control of the ball. It hits her arm, then her chest, then back off the arms, then she gets control. From the time it first hits her to the time she actually gets control of the ball she takes at least 4 steps, maybe even 5. The definition of traveling seems to imply the player has control of the ball, which a2 clearly did not have. What's the right call here?

There's no call. With one exception, you HAVE to be holding the ball in order to travel.

No control, no travel.

4.44 situation A

4.43 SITUATION A: A1 attempts to catch the ball while running rapidly. A1 muffs the ball, but succeeds in securing it before it strikes the floor. A1 then begins a dribble, taking several steps between the time the ball was first touched until it was caught. RULING: There has been no violation provided A1, after catching the ball, released the ball to start the dribble before the pivot foot was lifted from the floor. (4-15)