Fate is a funny thing; it doesn't have to be set in stone. When Sirius Black makes a different choice at that fateful night, the ripples from that decision affect Harry Potter and his friends. Yet, they didn't know that years earlier something else was also set in motion, which will also affect their lives and the magical world as a whole.
When Prince Zuko got banished from the Fire Nation, someone else decides to go with him. However, both of them can't imagine that huge powers are working in the background and meeting with the Avatar and his friends is just the start. The End of the future changes the present.