You cannot avoid probate with a Will. The only time a Will is ever effective is when it is admitted to probate. If there are assets titled in a decedent's name at the time of death, probate will be necessary. If assets are jointly held, (which is generally not a good idea), have beneficiaries designated, (a much better idea), or are held by a trust (also a good idea), then probate will not be necessary.
Everything else being equal, avoiding probate makes a lot of sense, in most cases.
Your parents should see an estate planning attorney to discuss their options. If they wish to avoid probate, a Will may not be needed, but they should both have durable power of attorney forms for financial and medical treatment matters.
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With or without a Last Will your parents assets would likely go through probate to be distributed. Often we attorneys would recommend a Living Trust to avoid probate.
More importantly, in my opinion, is the preparation of medical and property powers of attorney for your parents. Without them, in the event of incapacity, guardianship through court might become necessary. Guardianship proceedings are much more cumbersome and costly than probate.
I suggest that you do what you can to get your patents to chat with an elder law attorney to explain these concepts. You can find elder law attorneys on this website and at naela.org.
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You are receiving good advice in the earlier answers. When you ask what will happen, however, I assume the main question is who will receive those assets. Your parents may be surprised. If there are assets they hold individually, when the first of them first passes, the assets will go half to the surviving spouse, half to the children (including descendents of any deceased child), not all to the surviving spouse as many would envision. When the second dies, then assets will pass to the children or descendents of a deceased child. Another difference is that a bond will be required in the administration of the estate. So, there may be added costs or burdens on individuals. Also, things that you would think should be simply resolved and would be with a will, such as who should administer the estate, can blow up into added costs. As already advised, if nothing more, your parents should consider at least a simple will and powers of attorney for health care and property.
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