Thanks for your question.
I assume you are registered as tenants in common and not joint tenants.
If you are named as registered proprietor with your ex-partner and his father then they will require your consent to any transfer because you would have to sign the Land Registry Transfer form. If you are not willing to do this then they would have to apply for an order for sale of the property.
In the absence of any trust document to the contrary the presumption is that you own in equal shares, so there would be a presumption that you own 25% (with your ex-partner's woman passing to your ex-partner). This can be rebutted to an extent if you are not paying any of the mortgage payments , but it is not easy and it would require litigation by your ex-partner and his father so you should not agree to transfer without receiving a fair price for your equity.
You cannot transfer your interest to your children at the present time because in order to do so the mortgage company would have to consent to the transfer and they are not likely to do this. The transfer cannot be registered without their consent and children are not permitted to own a title in land if under 18. What usually happens is that the property is written in trust for them by the parents in the form of a bare trust.
You are of course free to write your Will so that your interest passes to your children upon your death. It would be held on trust for them until they are of age.
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