The other members of the Bat - family, like Robin (if it's not Tim at the moment), Nightwing, etc., would also be affected. They might split up to search for him. Some might feel angry at him for leaving without a word, while others would be more understanding and worried. For example, Alfred would be very concerned and would try to keep the family together during this difficult time.
It could make Batman more determined to find him. Batman would be worried about his safety and would start an intense search. He might also feel guilty, thinking that he could have done something to prevent Tim from running away.
Spike would be heartbroken. He's like Twilight's little brother. He depends on her for guidance and love. If she runs away, he might try to find her on his own and in the process, grow up a bit as he faces challenges alone. He could also feel abandoned and struggle with his own self - worth.
For Aunt May, it would be a huge shock. She has already lost so much in her life, and Peter running away would make her feel like she has failed in some way as a guardian. She would probably be constantly looking out the window, hoping to see him come back home. Also, the villains in the story could see his absence as an opportunity. They might become more bold and start causing more chaos in the city, knowing that Spider - Man is not around to stop them.
His friends will surely be worried. They might start looking for him everywhere, feeling sad and confused about why he left. For his closest friends, it could be a very emotional time as they fear for his safety.
For the other members of the Bat - family, like Dick Grayson or Barbara Gordon, it could create a rift. They might be caught in the middle between Tim and Batman. They may also start to reevaluate their own positions in the Bat - family, wondering if they too should consider leaving or changing their roles.
It can also change his relationships. Maybe he becomes more distant from his friends at first because of his loneliness, but then as the story progresses, his friends notice the change and try to reach out, which then becomes a major part of the plot as they try to heal his loneliness.
It could cause a sense of loss. Harry is a symbol of hope for the wizarding community. His running away might make some people feel abandoned.
For her family, it could be a shock. Her parents might feel sad and regretful that they didn't have a closer relationship with her so that she could confide in them. Her siblings might also be affected, perhaps feeling a sense of loss or confusion.
The other young members like Robin (if there's a new one) or Batgirl could be affected in terms of their own development. They might start to wonder if they should also consider leaving at some point. And it could create a sense of instability within the group as they have to adjust to not having Tim around.
It could make them realize how much they've taken her for granted. They might have been so focused on their gifts and their own roles that they didn't notice Mirabel's pain.
Tim Drake walking away in fanfiction could be a way to explore his character in a different light. It could show his independence. He might be walking away to start his own journey, to figure out who he really is outside of the shadow of the Bat - family. In some fanfictions, this could lead to him developing new skills or making new allies. It gives the writer a chance to take the character in a unique direction, away from the more traditional storylines.