What makes a will valid?

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My husband's widowed mother died without a will. Then one of his siblings found a scrap of paper on which their mother wrote that she gives her houses to two of her children and her bank account to her grandchildren and great-grandchild. Her two other children (one of them is my husband) apparently get nothing. When someone dies intestate, isn't an administrator appointed to oversee distribution of the assets? Don't they have to be equally distributed? If the two siblings who get nothing don't contest this "informal will," can the other two take everything?
You have the legal burden backward. The siblings who claim this paper is a will are the ones who must prove their assertion, says John Barnosky, a Uniondale estate lawyer. But you've accurately described what happens when a person dies intestate: If your mother-in-law left no will, by law her assets are equally divided among her children.
Any of her children can go into court and ask to be made administrator of her estate. The court sets a date to hear this request, notifying the other surviving children. At that hearing, they can present the scrap of paper as a will if they wish. It doesn't sound like one, Barnosky says. A scrap of paper saying, "This is what I'd like," isn't enough. To be legally valid, a will must in writing, signed by the testator and also by two witnesses.
Other readers, take note: Even simple wills are formal documents. Changes that you add to your will after you've signed it aren't legally recognized. And if you cross out several provisions, Barnosky adds, you may inadvertently invalidate your will; the court may conclude that you revoked it.
The bottom line: A will isn't valid until accepted by a court.

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