I just learned yesterday that Liv Tyler didn’t even know Steve was her father until she was around 11 years old. Apparently Liv’s mother (a former Playboy Playmate) had a fling with Steve and got pregnant, but didn’t want Steve involved in the child’s life because he was so heavy into drug abuse at the time. So she said the child was another former lover’s child, rock musician Todd Rundgren. Rundgren signed the birth certificate, and paid for Liv’s schooling. It’s not clear if he was aware that Liv wasn’t his or not. When Liv was around 11 years old she met Steve and immediately noticed how much they look and act alike. She confronted her mother who came clean about the ruse. Apparently Steve has been a good father ever since learning that he has a daughter, and they have a good relationship together.
Edit:
I just looked it up and apparently Rundgren realized there was a chance that Liv might not be his, but decided that she needed a father and he would fill that role. What dude being a man.