Well, in a Tim Drake Hogwarts fanfiction, he might be a transfer student. He'd be fascinated by the magic all around him, yet also a bit out of place. He could form an unlikely friendship with a house - elf, seeing their mistreatment as similar to the injustices he's witnessed in Gotham. And his intelligence would surely make him stand out in classes like Potions and Transfiguration. He might even try to combine his Muggle technology knowledge with magic, creating some interesting and potentially dangerous experiments.
One possibility is that Tim Drake uses his detective skills, which he has from his Gotham adventures, to solve mysteries in Hogwarts. Maybe there are strange disappearances in the Forbidden Forest and he teams up with the Hogwarts students to figure it out. He could also bring his martial arts skills to the wizarding world, perhaps teaching some of the more adventurous students a thing or two about self - defense.
Hermione could be one of his friends. They both are extremely intelligent and love to study. Hermione would be interested in Tim's knowledge from the Muggle world and they could exchange ideas about different subjects. Harry could also be his friend as they both have a sense of justice. They might team up to fight against the dark forces that lurk in Hogwarts.
Well, it could be about a lot of things. Maybe it's about a fractured or broken aspect of Tim Drake's life. It could be his relationships that are fractured, like with his friends or family in the Batman universe. It might also deal with his fractured sense of self, perhaps after some traumatic event.
Well, he might receive a mysterious gift that leads him on an adventure. Maybe it's a clue to a long - forgotten case. So he starts following the trail, which takes him all around Gotham. Along the way, he runs into some of Gotham's rogues who are also intrigued by the mystery gift. But in the end, he figures it out and it turns out to be a really special present from Bruce Wayne, like a piece of his father's old detective work.
Tim Drake's story also involves his relationships. For example, his friendship with the other members of the Teen Titans. One time, the Teen Titans were facing a powerful alien threat. Tim was the one who came up with a strategic plan. He analyzed the alien's weaknesses based on the little information they had. He coordinated the efforts of his friends, like having Starfire use her energy blasts at a specific time while Cyborg hacked into the alien's control system. Through their combined efforts, they defeated the alien and their bond as a team grew stronger.
It would be really cool. He could use his detective skills at Hogwarts, like solving the mystery of a missing magical item. Maybe he'd be a new student who's really into Muggle detective stories and uses that knowledge in the wizarding world.
Perhaps a plot twist could be that Tim Drake's angel - raised nature makes him an outcast among both humans and angels. The angels see him as too human, while the humans are afraid of his otherworldly upbringing. This could lead to him having to find his own place in the world, and in the process, he uncovers a conspiracy that links the two worlds more closely than anyone thought.
Well, in another universe, Tim Drake could be a villain instead of a hero. Maybe he had a different upbringing that led him astray. For example, if his family was involved in illegal activities, he might have been influenced by that and turned to the dark side.
In some fanfictions, it could be due to personal growth. Tim Drake might have outgrown the role of Robin or the shadow of Batman. He may want to explore his own identity and capabilities independently, away from the Bat - family. He could feel that staying with Batman is holding him back from reaching his full potential as a hero.
One possible reason could be that he feels misunderstood by his family or friends. Maybe he has some secrets that he's afraid to share, and the fear of being judged makes him run away.
Tim could end up saving Batman in the fanfiction. Despite being younger and less experienced, Tim might notice something that Batman misses during a fight. This would completely change Batman's view of him, and they could start to develop a more equal partnership.