To begin a basketball game, a tip-off is typically used to determine the first possession of the game. Then, in the second half, the team that did not start with the ball in the first half gets the first possession (or TeamA-TeamB-TeamB-TeamA format for a 4 quarter game).
For the purpose of this question let's assume a 2 half game, because it is overall simpler, but I figure the rule associated with this situation would be similar for a 4 quarter game.
What happens the player at the tip-off from one team (say Team A) hits the ball out of bounds off the tip, without it touching any other player? Does possession go to Team B? Additionally, if possession does go to Team B, does Team B additionally start with ball possession in the second half (as if Team A had won the tip-off normally and subsequently turned it over on the first possession)?