In some fanfictions, Hagrid and Harry's relationship grows when Hagrid starts to trust Harry with more important tasks related to the care of magical creatures. Harry, in turn, learns a great deal from Hagrid and starts to see him not just as a friend but as a true guide in the magical world. This development can be really interesting as it shows different facets of their personalities and how they interact in new situations.
In the original story, Hagrid is more of a secondary figure in Harry's life. But if he was raising Harry, their relationship would be much more paternal. Hagrid would be the one Harry turns to for all his problems, big or small. Harry would probably be more influenced by Hagrid's love for magical creatures and have a deeper understanding of them from an early age.
Harry would likely be more in touch with nature. Hagrid's love for magical creatures would rub off on him. He'd be less intimidated by the Forbidden Forest and might even see it as a second home. His values would also be more centered around loyalty and kindness in a simple, straightforward way like Hagrid's.
In many fanfictions, their relationship develops through shared danger. As they both fight against Voldemort's forces during the Deathly Hallows events, they rely on each other more. For example, Ginny might join Harry on some of his Horcrux - hunting missions secretly, and this shared experience brings them closer.
They might start off as just friends going into the room to study or find something for their next adventure. But as they spend more time in the room, sharing secrets and relying on each other, their bond deepens. For example, if they're in the room trying to solve a mystery, they'll have to trust each other completely, and that can lead to a stronger emotional connection.
It would likely be different in that Harry wouldn't rely on Hagrid as much for his initial introduction to the magical world of creatures. Since Charlie is already an expert in that area, Harry would probably have a more equal relationship with Hagrid. Instead of Hagrid showing Harry all the ropes about magical creatures, they might share knowledge and experiences more as peers.
In fanfiction, when they cuddle at the Burrow, it allows them to be vulnerable with each other. Harry, who has had a tough life, can relax and open up more to Ginny. Ginny, in turn, can show her support and love in a very intimate way. This sharing and closeness during cuddling helps their relationship to mature and become more stable. For example, they might cuddle while discussing their future, which is a big step in any relationship.
In some fanfictions, their relationship develops as they both deal with the loss of Peter Parker. They find comfort in each other and gradually realize they have deeper feelings. Harry might start to see Mary Jane not just as Peter's girlfriend but as someone he truly cares for on his own. Mary Jane, in turn, sees a different side of Harry as he matures and tries to move on from his past issues.
Often, they start with a surprising revelation of Hagrid's pregnancy. Then, they might focus on how Hagrid adjusts to his new situation. For instance, he may have to change his daily routine at Hogwarts.
In fanfiction, Hagrid often helps Harry by providing emotional support. He's always there with his big, warm heart to cheer Harry up when he's down. For example, after a tough encounter with a bully at Hogwarts, Hagrid might give Harry a big bear hug and tell him not to let the bully get to him.
It would likely strengthen their bond. Hagrid loves all magical creatures, especially dogs like Fang. Harry could share what the dogs are thinking and feeling, which would give Hagrid a whole new perspective on his beloved animals.