Travel or not?
 

High School rules situation. A1 bats the ball from B1. A2 picks up the ball at half-court and has a clear path to his basket. In stride, he throws the ball out ahead of him (it bounces first around the free throw line), where he then dribbles the ball once before his successful layup.
I haven't seen this before. It looked like a pass to himself. What would your decision have been if you were reffing? Travel or two points?

Two points.

Throwing the ball to the floor is a legal way to start the dribble. There is no restriction on the distance between the player and where the ball hits the floor (aside from being inbounds).

There's no rule against a "pass to himself." The only applicable rules are traveling and dribbling rules. Unless he picked up his pivot foot (while in stride) prior to throwing the ball to start his dribble, he didn't break any rules.

There's no such animal as a "pass to himself." Read the defintion of a pass. It's throwing the ball to a teammate. As Camron said, it's simply the start of a dribble.