The courts will look at any COA around what is in the best interest for the child, not the parents.
You've said you are currently preventing any contact. What was any previous contact? How old are the children involved? What led you to stop the contact? Have you been offering any alternative so indirect contact, contact with a third party doing the handover so you don't need to be present, day/evening contact instead of overnights?
Regarding the abuse - was he abusive towards you or the children directly or even both? If he's been abusive towards you, you can offer to communicate regarding the children using a court approved communication app such as AppClose. This means you can still keep him blocked on your phone but make dad aware of any emergency or welfare/health concerns. Likewise he can do the same.
He won't be able to apply directly for a COA in court unless he attempts mediation first UNLESS there's something to meet the criteria of bypassing such as abuse or harm to the children in your care. If he is currently withheld from being able to communicate, they may bypass mediation but that depends on the court and what he puts in the application to them (which you will get a copy of). If you do get invited to mediation, I would attend personally. The first session will be just you and the mediator so you can discuss your concerns re the abuse and if they feel it's needed & mediation isn't going to be safe, practical or right, they will sign the paperwork for it to go right to court.
Obviously without knowing the abuse element and who it was to, it's hard to reassure you that he won't get 50/50 but if you are seen to be obstructive, you could loose them altogether and dad issued the lives with order and you a spend time with. If the abuse was to you, they will likely permit contact between dad and children but if abuse was to children, then they will look at the impact and risks.
My own DSD9 has no direct contact with her mum as per ordered because mum subjected her to emotional abuse whilst also allowing her to be S.abused by her now ex-partner. So just because he's not there & they are no longer in a relationship, the courts listened to SDs impact via the reports done and decided the risks for further harm were way too great that even a contact centre wasn't deemed safe.