Survivorship means that if you have a joint account with someone else -- a business partner, your spouse, your parent -- and one of you dies, the other account holder inherits full ownership. If there are multiple account holders, the deceased's share is divided among all of them. Survivorship can have a big effect on inheritance and estate planning.
When an account, or any other jointly owned property, comes with the right of survivorship that trumps anything in the owners' wills. If you have a right of survivorship on a joint account with your mother, all the money in the account goes to you, even if her will says her property should be divided among all her children. This applies even if all the money in the account came from your mother and you didn't add anything to it.
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Your state statutes may dictate the requirements for setting up a joint account, and your bank may have its own paperwork you have to fill out. Make sure you fill out all the paperwork exactly the way it's supposed to be, and make it clear to the bank officials you deal with that right of survivorship is involved. If your relatives contest your right of survivorship in court, any deviation from the requirements could lead the judge to rule against you.
Setting up a joint account has advantages: If your parent is having mental difficulty keeping track of bills, a joint account gives you the power to write the checks for her. It has drawbacks too: A joint owner can legally empty the account, not only of her contributions but her co-owner's deposits, too. It's also vulnerable to the creditors of either owner, and it could be seized in Chapter 7 bankruptcy to pay one owner's debts.
A joint owner doesn't have to accept the benefits of survivorship. If you have right of survivorship on your mother's account, for instance, you can share the money with your siblings after her death. With a large account, this could trigger gift taxes, as well. You can avoid that problem with a disclaimer form waiving the right of survivorship. With a disclaimer, the account becomes subject to your mother's will, to be distributed with her other property.