Have you contributed financially towards the property? Have you done any decorating or improvements, gardening et cetera?
Did he ever promise that the house will be yours or part of it if ever you broke up or he died?
If he dies but never got divorced from the previous wife, then she would get a substantial share of whatever he leaves.
If he doesn’t have a wife, and only have one child, then everything would go to your son. You would get nothing. The law does not recognise a common-law relationship.
You may be entitled to some money from the house even though it is in his sole name, if you can prove that you contributed towards it. If you didn’t contribute to the fabric of the house or anything of any substantial value, then you have little claim.
If however, you had paid for the kitchen or improvements or suchlike, but it does give you a more substantial claim. Other than that, you don’t acquire a right to a share of the property just because you have been together for a protracted period of time.
If he had promised you the house if you stuck together with him, you may have a claim in Promissory Estoppel which is a technical legal doctrine where you can enforce the promise if you can prove the promise was made and that you relied on it to your detriment. You don’t mention that here.
You are both under a duty to provide a home for dependent children until aged 18 and hence, it’s unlikely that he would be able to get you out of the house (depending on the value of it), if you did split up, for another 3 years because of the need to provide a home for your son.
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