Dear Jamaica, you (I assume) asked a very similar question a few minutes ago from "Brooklyn". Check the answers in both threads and be patient. It takes up to several days or even a week while questions are active on Avvo to get them seen by attorneys who have subscriptions and get answers and sometimes different advice and perpectives on your issue. Creating multiple threads on the same question actually hampers this process and confuses things.
But the bottom line is still the same, you have a complicated question and need to see an estates attorney and find a will if your partner had one. Without that you are probably out of luck as the intestacy laws (for people without wills) aren't going to consider you as a "spouse" or "civil partner".
And whether you paid for things jointly is irrelevant. Mere roommates don't get to inherit unless they're on the decedent's deed in a certain, specific way discussed in the other thread or named in the will. Look for a will and hope your partner was prudent enough to have one. Look through his papers and see whether he's ever consulted an attorney on this, that's where the will may be (attorneys often keep them in special office files).
Dear how do I prove?
You did not mention whether your partner was one of the named persons on the deed, or who the other person is.
If your partner wanted you to own his share of the home, unless the deed was held in a manner so that the surviving named owner took all, he may have left you his interest in his will.
If there is a will and you are a beneficiary of his interest in the house, at some point the executor of the will will need to arrange that you receive title to his interest.
You should visit an attorney with all your papers.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.