Use dice to resolve who deals. In TtA , the player who played last breaks ties. If tied in Galaxy , check cards held. Each card for a world still in play counts double its face value. Other ship cards count their face value.
Highest total wins ties.
If still tied, player who played last wins. In TtA , the rules are very poorly written. In Galaxy , the rules are pretty clearly written, with a lengthy portion of a sample game. On p. 17, the last paragraph, Yellow does not get an attack opportunity, despite what they say.