Common law separation, how does this work?
You probably need to get some legal advice. If you hold the house as joint tenants you are entitled to half of the equity each. This cannot be altered by the courts because you are not married. There are other solutions, you could accept a lump sum now and have a charge on the property so that you can secure a further lump sum in the future Otherwise, house would have to be sold, perhaps she could investigate getting some sort of shared ownership property so that she does not have to waste her share. You have no legal responsibilities to her or the children. There is no such thing as a “common law” relationship. It was made up by the tabloids. It would be different if you were the father of the children.
