Well first of all if you are joint tenants as most people are it is not quite as simple as that .... you can elect to become tenants in common and then you will own exactly half of the house (or whatever part you specify) but there are lots of imponderables here i.e what is your partner's view, will they buy you out, will there be a legal battle over how much you are entitled to etc. etc. You need legal advice
And you need to consider if there is any mortgage outstanding. Say the house if worth �200k with a mortgage for �190k. Then there is only �10k of equity and if you are walking away from the mortgage too, why should you get �100k?