Legal end of a dribble?

[gslefeb]

I answered that it was a violation. There is a case saying touching a second time without the ball touching the floor is a violation.

4.15.4 Sit D This case talks about touching it a second time - not catching. So not 100% the same play.

My thoughts:
1. Tapping over the head and touching a second time is a double dribble violation.

2. Tapping over the head and allowing the ball to strike the ground is legal.

3. Tapping over the head and running several feet and catching is a travel, as the original tap ended the dribble? Or does the catch count as a second touch, therefore it is a double dribble?