If they die intestate (without a will) there is a statute in New Jersey that dictates how their estate will be divided. It will be a bit more difficult because they own property in France, and I have no idea what the law in France will require them to do. In New Jersey, when the first of them passes, the surviving spouse can become the administrator of the estate. This is the statute:
3B:5-3. Intestate share of decedent's surviving spouse
The intestate share of the surviving spouse is:
a. The entire intestate estate if:
(1) No descendant or parent of the decedent survives the decedent;or
(2) All of the decedent's surviving descendants are also descendants of the surviving spouse and there is no other descendant of the surviving spouse who survives the decedent;
b. The first 25% of the intestate estate, but not less than $50,000.00 nor more than $200,000.00, plus three-fourths of any balance of the intestate estate, if no descendant of the decedent survives the decedent, but a parent of the decedent survives the decedent;
c. The first 25% of the intestate estate, but not less than $50,000.00 nor more than $200,000.00, plus one-half of the balance of the intestate estate:
(1) If all of the decedent's surviving descendants are also descendants of the surviving spouse and the surviving spouse has one or more surviving descendants who are not descendants of the decedent ; or
(2) If one or more of the decedent's surviving descendants is not a descendant of the surviving spouse
You will fall into category (c) because there are three adult children and I am presuming that you are all children of both parents, not children of previous marriages. If would most likely be a lot easier to administer the estate if they had a will. They may also have certain tax advantages if they have a will that they will miss if they do not.
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