This section is from the book "Real Estate Principles And Practices", by Philip A. Benson, Nelson L. North. Also available from Amazon: Real Estate Principles and Practices.
One who dies leaving no will, is said to have died intestate. Such property as he may have owned at his death passes to his family by operation of law. The rights and priorities of the persons entitled to share in his estate are fixed by law in the several States. Those to whom the real property passes are termed heirs, while those who take the personal property are called next of kin. The widow curiously enough while she takes an interest in both the real and personal property is neither an heir or next of kin. As to the real property, if there be a widow, it immediately becomes subject to her dower rights. If there be children of the deceased owner, the realty is divided among them in equal shares, if they all be living. Should any of them be dead leaving children, such children divide equally the share their parent would have taken if living. For example; The deceased had four children, A. B. C. and D. A. B. and C. survived him. D predeceased him but left two children who were living at the death of their grandparent. A. B. and C. each receive one-fourth and the two grandchildren each one-eighth. If there be no children or issue of deceased children the property goes to the parents of the deceased and his collateral relatives i.e. brothers and sisters and their descendents in accordance with the law of the State in which the property is situate.
 
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