New Zealand Law
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He does have some rights to the house, but I would not recommend you let him move in, as he will be difficult to evict, because of his ownership share.
But the share he owns should be dealt with and you should enter into negotiations to pay him out, if he will do that, and if you can afford to buy him out. If he refuses to negotiate then the property may need to be sold
The situation is covered under the Property Relationships Act, which provides for equal shares in property so there is a risk he may claim more than the 20% share which you are talking about. So whatever is done you need a clear and binding agreement about interests in the property and I suggest you urgently see a local family lawyer to start the process of dividing the property