He'd be frantic. Tony loves his daughter deeply, so he'd immediately start searching for her. He'd use all his resources, his technology, and his connections to find her.
At first, he might be angry, thinking she's being irresponsible. But then, as he realizes the possible reasons for her running away, he'd be filled with guilt. He'd blame himself for not being there for her enough. He'd probably stop at nothing to get her back, and when he does find her, he'd be very emotional. He'd hug her tightly and promise to be a better father, to listen to her more and give her more space if that's what she needs.
Tony would be in a state of shock. His daughter is his world, and her running away would be like his worst nightmare coming true. He'd likely go into a bit of a self - destructive mode at first, blaming himself for every little thing he might have done wrong. Then, he'd pull himself together and start a very methodical search. He'd enlist the help of the Avengers, his friends like Pepper, and anyone else he could think of. He'd be constantly worried about her safety and well - being until she's back home.
Well, she might run away because she feels overshadowed by her father's fame. Everyone always talks about Tony Stark, Iron Man, and she may feel like she's just an afterthought. Maybe she wants to find her own identity away from the Stark name.
He would be extremely worried. Tony Stark, despite his tough exterior, loves his daughter deeply. He'd probably start by using all his resources to find her. He has access to advanced technology, so he'd likely use his Stark Industries gadgets to track her down.
He'd probably be shocked at first. Tony is always so caught up in his own world that a secret daughter would be a huge surprise. But then he'd likely be protective. He might try to keep her away from his dangerous life at first, but as he gets to know her, he'd start to include her in things.
He would probably be overprotective at first. Tony has been through a lot, and the idea of his daughter having mutant powers, which could make her a target, would be scary for him. He might try to keep her locked away in the Stark Tower, but that would likely lead to her rebelling.
In fanfiction, she might run away because of a misunderstanding. Maybe she overheard something she wasn't supposed to and misinterpreted it. For example, if she heard her father talking about some kind of protection plan for her that she thought was him trying to control her life more. It could also be that she has her own secrets, like developing powers that she's afraid to tell her father about and decides to run away to figure things out on her own.
Another idea for this fanfiction could be that Tony Stark's daughter starts as a sort of 'Avengers - in - training'. She is constantly trying to prove herself to the established members. There could be a lot of action - packed scenes where she is in dangerous situations but manages to use her wits and any skills she has learned from her father to get out of them.
Love and friendship are also common themes. Her relationships with friends at school or in the superhero community, and her romantic interests if any, are often explored. It gives a more well - rounded view of her character as not just a Stark, but also a young girl growing up in a complex world.
One popular type of fanfiction could be about Tony Stark's daughter joining the Avengers. Maybe she inherits his genius and creates her own high - tech suit. She might struggle at first to be accepted by the existing Avengers, like Iron Man did. But through her skills and determination, she gradually wins them over and becomes an important part of the team.
Tony could be initially shocked. He might not understand why Peter would run away, especially if they had a good relationship before. He'd probably start searching for Peter right away, using all his resources.
Pepper Potts could be a common character. She might be in a position where she tries to mediate between Tony and his unwanted daughter, either trying to get Tony to be more accepting or helping the daughter understand Tony's perspective.