Teloch asked: Headcanons on if Azula and Zuko ran away before Azulon's death and Ursa's exile.
The first thing that immediately comes to my mind is: my fucking God, these two are going to get themselves in ridiculous amounts of trouble on a daily basis. They're smart, strong kids so they'd eventually be okay, but the entire situation is going to be hell until they figure shit out.
I can see them constantly turning to each other for emotional support since they have no one but each other now, falling asleep in each other's arms, being super protective, and most important of all, they'd find a way to salvage their relationship with little to no damage since their rivalry didn't have the time to become as intense as it would be on their teenage years.
If they were found and brought back home, their bond would be so strong that I feel even Ozai wouldn't be able to put them against each other. If they weren't, then they'd probably develop an "Us against the world" mentality. Either way, by the time they're entering puberty they'd both be fully aware of their feelings for each other and it wouldn't take long for them to be officially together.