One great 'Aang and Katara and Zuko' fanfiction is 'The Fire and Water Alliance'. It delves into how they work together to rebuild the world after the war. Their different abilities and personalities create interesting dynamics.
You can start by looking on Archive of Our Own (AO3). It has a large collection of fanfictions including many about Aang, Katara, and Zuko. Just search for their names in the search bar.
One popular 'zuko x katara x aang fanfic' is 'The Elemental Bond'. It explores their complex relationships in a post - war world. The author does a great job of showing how they interact and support each other. Another one is 'Triple Alliance' which delves into their adventures together, with some interesting character development for all three. And 'Harmony Among the Elements' is also good, as it focuses on how their different personalities and powers can work together in harmony.
In these fanfics, the relationships usually develop through shared experiences. Maybe they go on a quest together. During this quest, they have to camp out, share food, and protect each other from danger. Zuko might show his more vulnerable side to Katara and Aang, which helps them to forgive his past wrongs. Aang, with his positive and open - hearted nature, can also help Katara and Zuko to be more in tune with their spiritual sides. And Katara's nurturing nature can heal the emotional wounds between them, leading to a stronger and more complex relationship.
Some fanfictions explore their role in rebuilding the world after the war. Zuko and Katara could be working together to restore balance between the nations. This kind of fanfiction often shows their leadership skills and how they complement each other.
Their relationship could deepen as they share in the joys and sorrows of rebuilding the world. They've been through a lot during the war, and now they can truly rely on each other. They might become even closer friends at first, with a mutual respect for each other's abilities growing stronger.
In some cases, the anger could be a catalyst for a more romantic development. Aang expressing his strong emotions might make Katara realize the depth of his feelings for her. Or it could be the other way around, Katara's reaction to his anger could make Aang see her in a new light, leading to a shift in their relationship dynamic towards a more romantic one.
It would likely become more complex. They would have to rely on each other more as parents. Their love might deepen as they share the experience of raising a child together.
Maybe Zuko has his own goals that don't involve chasing Aang. He could be more focused on redeeming himself in other ways, like helping the Fire Nation people or learning about different cultures without the need to pursue Aang.