As most of the people answering your question has said you will have to go through probate and in order to do this you will need an attorney. Most attorneys will give you free advice as to if you need to go through probate or not. Look in the telephone book under probate lawyers or ask a friend if they know one.
Good news, the attorney is paid after the probate is complete,so usually there is no up front fees.
In some states if the value of the property is less than a certain amount probate is not required.
If I was you before I contacted any of the people that your mother was in debt to I would seek the advice of an attorney. When going through probate, the court requires that a notice be filed in a local newspaper about the death and all that are owed should appear in court or send the debt to the probate attorney, who will give it to the probate judge.
Most attorneys advertise in a legal paper where the general public normally don't read. If no one lays claim to your mother owning a debt to them the court will wipe them out and they can not come after you after probate is closed. You will be required to pay only the ones that step forward and lay claim to your mother owning them, if any.
If any one step forward, claim your mother has a debt with them and the debt is deem legal by the court they must be paid by your mother's estate.
Once probate is closed you or your mother's estate will be required to pay the attorney a certain percentage of the value of your mother's property, in California it is 6%.
Once probate is complete the court will authorize the property to be placed in your name and a deed will be prepared by the probate attorney that must be filed at the county court. The attorney will probably give it to you to take to the county court to get it recorded, while you are there ask for a copy.
I hope this has been of some use to you, good luck.
"FIGHT ON"