Hello and thanks for your question.
The question of how much contact (if any) and what sort, that a father should have with their child is entirely unrelated to how much if any child support they pay. He could be a millionaire and have to pay a lot but be a nasty perosn who is not allowed to see his kid - or a pauper who is a great dad and gets to see his kids a lot.
The key point is what is in the child's best interest and how would her welfare be affected. Although in principle, it is government policy that children should have contact with the parent they do not live with, unless there are strong reasons why not, how that works in practice varies enormously from one child to the next. The contact could be face-to-face, ie direct, or indirect ie letters & cards only. If face-to-face,it could be supervised, or unsupervised.
In your case, as your daughter has not seen him for 9 years, if he is to have any contact at all, at most the court is likely to say that it should start with supervised contact for example at 1 hour per month at a contact centre, or the court might even say that it should start with a letter or card once a month for a few months, before progressing to a contact centre. So don't feel you have to agree to anything that wouldn't be right for your daughter, but do have some discussions with him if he asks for contact, to consider what would be appropriate eg maybe he could see her for an hour a month at your local MacDonalds supervised by either you or a trusted relative or friend?
Ultimately, if you can't reach agreement, then either one of you can apply to court for a child arrangements order, for the court to decide what his contact should be. But going to court is time-consuming, stressful and expensive. There is no longer any legal aid for this type of application to court, so if you can negoatiate something between you that's preferable. You can do that either via talking to each other or via solicitors' correspondence or via mediation. The family court anyway now requires the parties to have attempted mediation before it will consider an application to court.
Here's where to find a family mediation sevice near you:
And for some face-to-face legal advice, here's where to find a specilaist family law solicitor:
I hope this helps and I wish you the best of luck.
Thanks and best wishes...