It is not necessary to remove your father's name from the deed if they purchased the property as husband and wife. Such ownership is called a tenancy by the entirety. Once a spouse passes then that spouses share reverts to the surviving spouse. You should retain a copy of the death certificate to show proof of death when the house is sold. If there was money owed to a creditor and a judgment was obtained against your father then those liens would have to be satisfied before the house could be sold. I would strongly suggest that your mom prepare a Will so that ownership of the property can be administered after her death. A transfer for no or nominal consideration will not wipe out debts to creditors.
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If they were married at his death...no.
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You should look at the deed.
If both your father and mother are named on the deed and their names are followed by "Husband and Wife" or "H/W", then there is no need to change the deed. The words husband and wife on a deed create a tenancy by the entireties which means that your mother owns 100% of the property.
If the deed only has your father's name, then an estate deed should be filed to transfer the home to your mother.
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