What happens to a persons home if a person dies with a will or trust

When someone dies without a will, their property passes by "intestate succession," or the rules for who gets what when there is no will. In your state (CA), the surviving spouse gets all the community property (everything and all the money acquired during marriage, other than anything inherited by or gifted to the deceased spouse) and (when there are multiple chidren) 1/3 the deceased's separate property (anything he owned premarriage, or which was gifted to or inherited by him during marriage); the children share the other 2/3 separate property.
There are additional wrinkles: 
1) Certain assets of your father may go directly to your mother without regard to intestate succession: for example, if he and she owned a house as "joint tenants with right of survivorship" or JTROS, on his death, it automatically became solely hers.
2) Any heir who is willing to give up his/her inheritance can "disclaim" it and it will go to the other heirs. If all children disclaimed, your mother would get everything.
3) Any mortgages must be paid on real estate or any loans on cars must be paid or the property/car can be foreclosed upon or repossessed.
4) Other persons or business whom your father owed money can file claims against his estate (to be paid from the money, etc. he left behind).
The best thing to do is to hire a probate lawyer to help--the lawyer can examine how the different assets were owned, see what goes to your mother directly, and what is subject to intestate succession; can help any children willing to give up their shares to do so; can respond to any claims against the estate, or by mortgagees or auto lenders; and can do the paperwork to put everything she inherits into your mother's name.