New Zealand Law
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Under the Property Relationships Act this house would be relationship property and the starting point is an equal division, even though the contributions are not equal. What complicates your situation is that under section 24 of the act, any application for division of property must be made within 3 years of separation. But he has lodged a claim against the title within the three period, but hasn't taken any other steps. So he is bared from filing in court but will be difficult about removing the notice of claim, the caveat. So the value of his sore is at the time he applies to court but the amount of his share is as at separation. As he hasn't contributed to the overheads at all, and paid well under the market rent, his hare is likely to be much less than half. So you will need to consider making an offer to make him go away and I suggest start at about 10 to 20 % of the value as at now before you do any work on the property. But you could take a hard line and tell him he is out of time to claim anything.