Azir moving on his own
After I was about level 3 or 4, when I summoned Azir's soldiers and had them autoattack Azir would start moving in his attacking soldier's direction. If he bumped into a minion he was attack it at melee range, and if he didn't bump into anything he would stop where his solider was. Later on in the game, at about 13 minutes in, he would also randomly move towards the fountain. That didn't happen as consistently however.