The house will be split between both partners. It is best if you agree with your ex partner what will happen to the house (e.g. one partner could buy the other partner's shares, you could continue to jointly own it and rent it out and keep part of the rental income). If one party wishes to sell and the other does not, then that party may apply to court for an order to sell or order to partition and then it will be up to a court to decide. In this case, the court will consider the interests of the other (unwilling) partner and any third party interests.