I cannot tell from your recitation of the facts whether all three of you were joint tenants with right of survivorship, or just you and your husband. If all three of you were included with right of survivorship, then you would record your father's death certificate with the county recorder and you and your husband would own the property outright. It your father owned his interest in the house separately and only you and your husband owned as joint tenants, then you would have to probate as to your father's interest.
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I agree with Attorney Reed. You should be all right without having to go to court, as long as the QUIT Claim Deed says what you indicate it does. You may want to run this by a title company to make sure they will accept the deed.
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Upon the death of one party to property in joint names, the survivors own the property and can sell it, mortgage it, or do whatever they wish. They automatically become owners without probate, but need to file an "Affidavit of Joint Tenancy" to remove the deceased person's name from the title.
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Generally in Florida you should probate the estate, as an "intestate". The problem with sale is more one of buyers getting a loan to purchase a property and a title company may be unwilling to write insurance on the transaction. An order from the probate court alleviates the problem.
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