He could run away to a far - off wizarding village. There are many small, secluded villages in the wizarding world that are not well - known. For example, a place like Hogsmeade but much more remote, where he can start anew and not be bothered by his past or family.
They might choose to run away because they want privacy. After all the battles and saving the world multiple times, they just want some time alone without any interruptions from other demigods or the gods. So running away seems like a good option.
Perhaps they run away because they are tired of all the rules and expectations placed on them. They just want to be free and explore the world on their own terms. They could end up in a small, idyllic town where they learn more about normal human life and each other away from the chaos of the demigod realm.
In this fanfiction, Percy and Thalia could meet a powerful sorcerer who has been exiled from the magical community. The sorcerer could see potential in them and offer to teach them some ancient magic spells that could be useful against their enemies. Additionally, they may come across a group of forest spirits. These spirits could be initially hostile but after learning of Percy and Thalia's noble intentions, they could provide them with shelter and information about hidden paths that lead to safe places away from the threats they are running from.
In such a fanfiction, they might run away to avoid some great danger in the Camp. Maybe they discover a plot against demigods and feel they can't trust anyone there, so they set off on their own to find a way to stop it.
It could be that they run away to find someone. Maybe a missing demigod friend or a powerful being who can help them with a problem they're facing. Percy, Thalia, and Nico might have received a mysterious message or a vision that leads them on this journey. As they run away and start their search, they encounter various obstacles. They have to cross dangerous terrains, deal with unfriendly gods or demigods who don't want them to succeed, and also figure out how to work together effectively. Their friendship is tested, but in the end, they grow stronger together.
They could meet other demigods who are also on the run or lost. These demigods might have different powers and backgrounds, and together they could form a sort of 'runaway group'. For example, they might meet a demigod who has the power of controlling plants and can help them find food and shelter in the wild.
One reason could be to avoid a dangerous prophecy that they believe the camp can't protect them from. In some fanfictions, they might think that by running away, they can face the threat on their own terms.
Percy's powers might evolve in terms of his connection to the sea. Maybe he starts to communicate with sea creatures in a more profound way. He could ask for their help in escaping pursuers or finding food and shelter. Thalia's power over lightning could also be related to her emotions more closely. As she faces different challenges during their escape, her lightning bolts could become more powerful depending on her state of mind. Nico, on the other hand, might start to have more control over the undead. He could use them as scouts or to create distractions when they're in trouble. This evolution of their powers would be a result of the new and difficult situations they face while running away.
If their fight is really bad, it could create a rift between them for a while. They might avoid each other, which would be hard since they are usually so close. This could make it difficult for them to work together on future quests.