Batman's brooding and serious personality would likely make Harry more cautious. Batman is all about planning and preparation, and Harry would pick up on that. For example, Harry might start to analyze magical situations more thoroughly before acting, instead of just relying on his instincts.
In some 'Batman Adopts Harry Potter' fanfictions, a great plot is when Batman tries to enroll Harry in a normal school in Gotham. Harry has to adapt to a non - magical educational system while also hiding his wizarding past. At the same time, Batman is trying to protect Harry from any threats that might come from the wizarding world, like Death Eaters or Voldemort's followers who might want to harm the Boy Who Lived.
Perhaps Bruce Banner adopts Harry Potter after the events at Hogwarts. He takes Harry to the world of science, showing him things like advanced laboratories and scientific research. Harry, in turn, shows Bruce the wonders of magic. Their bond grows as they learn from each other, and together they face new threats that combine elements of both the magical and scientific worlds.
It could be a young wizard who lost their parents during the final battle against Voldemort. Harry feels responsible for all the orphans created by the war and decides to take this particular child under his wing.
Another theme is self - discovery for Harry. With the influence of the MC, Harry gets to explore different aspects of himself. For example, he might discover new magical abilities or gain more confidence in his identity as a wizard. In some fanfictions, the MC helps Harry to look beyond what he thought was possible for himself.
In the fanfiction, Batman might adopt the little girl because she shows extraordinary intelligence or a unique ability. For example, she could be a tech prodigy. This would attract Batman as he always looks for ways to enhance his crime - fighting capabilities. He would then have to balance his role as a father figure with his duties as Batman, which could lead to some interesting internal and external conflicts.
Well, one possibility is that Harry realizes Fenrir's tragic backstory and decides to help him change. Maybe he uses magic to suppress Fenrir's werewolf side and tries to integrate him into the wizarding society. Harry could teach Fenrir about friendship and loyalty, and together they fight against the dark forces that once exploited Fenrir.
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.
The combination of two very different universes. Ichigo from Bleach is a very different character from those in Harry Potter. His unique powers and personality, when put in the context of the wizarding world, create a lot of interesting scenarios.
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.