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I don't know if you should say "mediorce". The only reasons that Ozai favors Azula is that she's actually a firebending prodigy, and that she's more like her father, while Zuko can be seen as "weak" because he actually cares for the people of the Fire Nation.

As for their recent battles together, Katara is now a Waterbending master. Zuko has been learning Firebending from Uncle Iroh. Now, he's actually a match for Katara in terms of fighting, and she's a master! But, it all has to do with the time they fight. When it's during the day, Zuko's bound to win. During the night, it's the other way around.

Zuko and Katara have some other things in common. Both had to mature quickly in their situations. Katara had to because her mother was killed, and she had to do all the chores, and take care of Gran-Gran and Sokka. In their journeys, the trio had to fend for themselves, and try to evade the Fire Nation while going up to the north. Zuko had to because he was to be the heir of the Fire Nation throne. And, when he was exiled, he had to do a search for the Avatar, take control of a ship and it's crew, and all in all try to keep himself calm in all the pressure he has. Now he and Uncle Iroh are being hunted by family.

Not only that, him falling in love with Katara might bring him closer to the Avatar. But, since they can't go home anymore, and Azula's going to get everyone to not harbor the two, where are the two going to turn to?

And here's something weird: he somehow knows things about her. In "The Waterbending Scroll", he knew that it was Katara's necklace. And in the season finale, with their first fight together, Zuko says that he notices that she has some new moves. How did he know?

But then again, anything's possible. I ship Zutara, although I'd rather keep a neutral stance on the shipper war.

Zuko and Katara!!!!
I will hunt down and assassinate the creators of avatar if they make Katara and Aang a couple. I just completely disapprove of that coupling. I feel that Katara is more of a motherly figure for Aang, not only that but I feel that Aang is too childish for Katara. Then also they are like colleges. It just wouldn't be right in my opinion.

I feel more comfortable with Zuko and Katara, I like intense romance, and I would guess that it would be VERY intense between Zuko and Katara [not in a kinky way] Intense as in they are almost exact opposites. The two are at each other throats, now that would make a sexy romance!

But then most of the time he is more focused on Aang than the other two. Not only that, he hasn't really seen much of her Waterbending moves before "The Seige of the North", except for "The Waterbending Scroll" and "Bato of the Water Tribe". If he was really focused on Aang, then a memory of seeing Katara with a necklace would be faded away with all the sad memories of his past, capturing Aang, wishes of going back home, and having to deal with a whole crew and now being hunted by a sister.

And his quest for the throne, well, even though Zuko's smart...he gets really stupid sometimes, for example, believing Azula's lie. And for now, that quest is probably on the side because now Zuko and Iroh are now being hunted by Azula. No one can help them now, unless they want to be in trouble with the Fire Lord. Probably the only people that could help them and could care less of the Fire Lord is the Avatar trio. Especially Aang, since he wants to be friends with him. Not only that, friendship with the trio and a relationship with Katara would lead him closer to the end of his quest. Why? Because if they do join the gang and go to the Fire Nation, he could just be like "Okay, father, I've got the Avatar now. Can I have everything I lost back?" Well, although Ozai would care LESS if Zuko was dead.
And if they do join, hopfully the trio and Iroh will knock him into his senses and see that his father and family doesn't want a dishonorable guy like them back. And that probably the only way to get the throne is to overthrow his own father and sister.

Well, there is obviously no one in the Avatar world who can bend multiple elements except for the Avatar. So, their children might be either a Firebender or a Waterbender. Or, because fire and water naturally go against each other, one might be a non-bender.

I was thinking of writing a story that took place in the future, and yes, Zuko and Katara are the now Fire Lord and Lady in the story, while Aang marries Meng. Zuko and Katara have two children: the eldest is a female firebender, while the other is a male waterbender. They have to send him to either the North or South pole for him to escape discrimination there and for him to meet other waterbenders as himself.

Oh goodness. You've initiated a battle between the two almighty ships XD.

Anyway, I feel like Aang and Katara are more likely, but I'm hoping for Zuko and Katara. Why? Because Zuko deserves LOVE! I'm tired of everyone ruining his life, he needs someone to help make him happy! For some reason I think Katara can do that because I think he'll have more respect for her now that she's beaten him and that they saved him in the blizzard. I've never really believed in the term "opposites attract", but in this case I'm hoping it'll work. I'm tired of seeing my favorite characters be lonely and sad. I want Zuko to be happy and for his story to end in a nice way.

Aang and Katara. It just has to be. Zuko and Katara may have their moments, but Aang and Katara will eventually happen....

*Sigh* The worst couple, Aang and Kat, is most likely, but that doesn't mean I can't hate that couple with every fiber of my being. That's why I'm a huge Robin/Raven shipper (Teen Titans). Rob/Star sucks, even though it's most likely.
Anyways, Aang is too much of a little brother to date Katara, and Zutara makes more since.