If property is held in joint tenancy, you will have to file an affidavit of death of joint tenant with the county recorders office. If held differently you will have to do other things. Since you are on the mortgage, nothing should be needed to be done with that.
No, nothing happens to the mortgage since you are both responsible, but you will be solely responsible, if your father's estate cannot pay it; title depends om how it is currently titled.
The foregoing is for informational purposes only and may not be relied on as attorney-client advice.
It depends on how you are holding the property and what his will says. If you hold the property as joint tenants then on his death the property belongs to the survivor, the last to die. If the property is held as tenants in common, then his will determines who gets his property including this house.
His marital status could affect this issue too, but. You did not include that in your question.
The portion of your question that is visible asks two distinctly differnt questions.
First, title to the property is determined by the deed conveying the property to you and your father. As Mr. Gross briefly pointed out, if the property is held in joint tenancy, you will take title by recording an affidavit of death of joint tenant covering a certified copy of his death certifcicate. If your father's interest is held in his trust, then the successor trustee takes title to his interest by filing an affidavit of death of trustee. If the property is held as tenants in common, upon his death, his interest will be disposed of according to his will, if he has one, or by the rules of intestate succession. In short, the answer to your first question requires a lot more information, with which a qualified real estate attorney can advise you.
The second question is easier. Upon your father's death, both you as an individual and your father's estate will be jointly liable for the mortgage. If your father's estate is solvent, You could require his personal representative, executor, or successor trustee to pay your father's share of the obligation.
If your father's estate is insolvent, then you will become liable for the mortgage.
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