The girl might be an outcast in the wizarding world, perhaps because of her family's past or her own unique appearance. Harry, being the kind - hearted person he is, decides to give her a home and a family. He sees potential in her and wants to protect her from the cruel world.
She could be a young girl who has lost her parents in a magical accident. Maybe she has some special powers that Harry notices and that's why he decides to adopt her.
The girl might be a descendant of an old wizarding family that has fallen on hard times. Harry adopts her to revive the family's honor. She could have some special knowledge or heirloom that attracts Harry's attention and makes him decide to take her in.
One possible plot is that the girl is from a non - magical family but has a deep fascination with Harry's story. Harry discovers her and decides to adopt her as she has a natural inclination towards magic. He trains her privately at first, and as she gets better, he reveals her to the wizarding community. Along the way, they face some challenges from those who are against a Muggle - born being trained by Harry, but they overcome them together.
She could be a descendant of one of Fry's friends in a really convoluted time - travel related scenario. Maybe she's related to Bender somehow, and that's part of the reason Fry feels obligated to take her in.
Perhaps the girl is a huge fan of Harry Potter in the fanfiction world. When Harry discovers her, she's being bullied for her love of him and his story. So, he adopts her to protect her. He then shows her the real Hogwarts, not just the one she's read about. Along the way, they might face challenges from those who don't like the idea of Harry having an adopted daughter, but they overcome them together.
There could be Lou, Ty's friend or colleague. She could play an important role in helping the girl adjust to the new environment, perhaps by taking her shopping for new clothes or showing her around the place. Another character could be Grandpa Jack, who gives the girl some valuable life lessons based on his own experiences.
It could be Ginny Weasley. Since they have a relationship in the original series, it's not too far - fetched to imagine a scenario where she gets pregnant. Maybe they got carried away during a time of peace in the wizarding world.
It's possible that the little girl's presence would soften Batman's tough exterior. He's always been this brooding, dark figure, but having a daughter - like figure in his life could make him more approachable and show a different side of him to the people of Gotham.
Maybe in the fanfiction, Ty Borden has always wanted a family of his own. He meets this girl who has a special connection with horses, just like him. He adopts her and they start to build a life together on the ranch. They face challenges such as financial difficulties in taking care of the girl and also some opposition from people who don't think Ty is a suitable guardian at first, but they overcome all these together.
Well, it could start with the little girl being an orphan from a destroyed village. Naruto, having experienced similar pain, feels a strong connection. He adopts her and as she grows up, she becomes a source of pride for Naruto. She might also have some unique abilities that Naruto helps her develop while also protecting her from those who might want to use her powers for bad.
It could be a group of rogue ninjas who are after the cat girl for some special power she might possess. They see Naruto as an obstacle in their way to get to her.