Have the partner throw in the proverbial dollar / Euro and make sure there's paperwork. Ie, you own 99.99% (or somesuch) and your partner the rest.
Not sure if a co-habitant would need to pay a notional "benefit in kind" tax.
Is it tax relevant if you have someone else (who is not your spouse) living in your house without charging rent
If you're paying 100% of the cost of the house and she's getting a 50% share in it — yes, she's liable to Capital Acquisitions Tax on the value of the 50% share, which is treated as a gift from you to her.
Talk to a lawyer or accoutant about ways of reducing this tax exposure before you commit to any course of action.
In principal, if you provide someone with free accommodation, that's a gift. The value of the gift is the rent they would have to pay in the open market for accommodation of that kind. You're liable to capital acquisitions tax on the value of the gift.
But . . .
Nearly all of the discussion and case law about this involves situations where someone is given the exclusive use of a house, or a room in a house. If you simply have someone staying with you as a guest in your home, even a long-term guest, I don't think Revenue would expect that to be reported or would charge it to capital acquisitions tax.