If a person dies in the state of Ohio without a Will, they have died intestate. The Probate Court will then use the “Statute of Descent and Distribution” to determine who will receive your assets.
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Single with children – All to your children. If one of your children has predeceased you, their share will go equally to their biological and/or adopted children.
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Single with no children – All to your parents. If both parents have predeceased, to their children (your siblings). If any of your siblings have predeceased you, their share will go equally to their biological and/or adopted children.
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Single with no children, no parents, or no siblings – One half to maternal grandparents and one half to paternal grandparents. If all grandparents have predeceased you, their share will go equally to their biological and/or adopted children.
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Married with no children – All to your spouse.
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Married with all children joint with your spouse – All to your spouse.
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Married with one child who is not your spouse’s child – The first $20,000, plus a spousal allowance of $40,000, plus ½ of the remaining assets to your spouse and ½ of the remaining assets to your child.
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Married with more than one child and your spouse is the parent of at least one of the children – The first $60,000, plus a spousal allowance of $40,000, plus 1/3 of the remaining assets to your spouse and 2/3 of the remaining assets to your children.
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Married with more than one child and your spouse is not the parent of any of your children – The first $20,000, plus a spousal allowance of $40,000, plus 1/3 of the remaining assets to your spouse and 2/3 of the remaining assets to your children.
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If no living next of kin – To stepchildren. If one of your stepchildren has predeceased you, their share will go equally to their biological and/or adopted children.
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If none of the above – To the State of Ohio.

There are ways to avoid Probate, but these should be discussed with an attorney to determine your best options.