It's that way here in Canada too. I thought it was different in the UK, sorry.
It happened to my donor, actually, after my youngest, and it made him reluctant to donate to me again. He actually stopped donating, but he agreed to donate to me again, and I'm glad he did cuz my daughter has a full sibling instead of just half-siblings.
He did contracts, and they had agreed that he would never come after custody or access, but that the child could contact seek to meet him when he turned 18, and that if any medical issues came up with the child, that he agreed to provide blood for any DNA testing needed.
Anyway, I guess everything was fine until the child was about 4 and then the mother could no long financially provide for the child and she decided to go against the contract and had him tracked so that she could sue him for child support. He thought he was safe because of the contract but sperm donation outside of a clinic in Canada is actually illegal and the court decided that regardless of the contract, the rights of the child came first and he was ordered to pay child support but when he requested daytime visitation with the child he was now paying for (since the contract was apparently void in court), the judge denied him the request claiming he had purposely abandoned the child and that it would be damaging to the child's wellbeing.
So, I understand why he then decided to stop donating. He's never had any other issues with any of the other women. He's donated to only two women more than once. Although I WAS kind of disappointed to learn that this baby is number 9 for him. He lives two hours away, and the majority of kids live around that area, but it just makes it that much more difficult in the future with my daughter when I tell her. How do you tell a young woman going off to college that she has to be careful if she finds a guy that is part Armenian because it might be her brother? (Of the 9, only 2 are girls)