One possibility is that Percy arrives at Annabeth's parents' place and is immediately awed by their grand home. He shakes hands with her father firmly and looks her mother in the eye. They might ask him about his adventures, and he'd share some of the less dangerous ones to make them feel at ease. Then they could all sit down for a meal, and Percy would try his best to use proper table manners, all while Annabeth is giving him encouraging looks.
Percy tries to be on his best behavior. He listens carefully when her parents talk, and answers their questions honestly. He also makes sure to compliment their home or any work they've done. He might even offer to help with something small, like setting the table if they're having a meal together. This way, he shows that he's not only interested in Annabeth but also in being part of her family in a way.
In the fanfic, Percy might be really nervous when he meets Annabeth's parents. He could be worried about making a good impression. Maybe he tries to be on his best behavior, like being extra polite and respectful.
In this kind of fanfiction, they might have an adventure together. Maybe they'll face a new monster that they haven't encountered before. For example, a mythical creature from a less - known part of Greek mythology.
Their relationship is likely to be complex. They are friends and comrades who have fought side by side many times. So, there's a strong bond of loyalty between them.
The main characters are Annabeth and Percy, of course. They are central to the story in the fanfiction just as they are in the original Percy Jackson series.
Well, it could be that Annabeth and Percy meet in a different setting than in the original stories. For example, they could meet in a modern city but still have to deal with their demigod issues. They might discover new powers or abilities within themselves as they interact. And there could be some romantic moments as their relationship often has that element in fanfictions.
Often, it could be old enemies like the Titans. In fanfiction, they might return in new and more devious ways. For example, Kronos could have a new plan to break Percy and Annabeth apart before trying to take over the world again.
The 'famous Percy' could be a super - fan who has made a name for himself by creating amazing fan art of Percy. When Annabeth meets him, she is impressed by his creativity and how well he has captured Percy's likeness in his art.