When it comes to setting up your will or your trust, a lot of people have a common belief that if you want to disinherit someone, you still leave them a dollar. I don't believe in drafting a document with this provision. I think you are just inviting problems. Especially if your estate planning document is a trust. With a trust, only beneficiaries of the trust receive notification that they are a beneficiary and leaving them even just a dollar brings them into the process. My recommendation is that you specifically exclude them altogether and make that very clear within the document.
If you are setting up a simple will and you specifically exclude a natural heir of your estate (child, grandchild, sibling) they may still be entitled to notice of the proceeding under the probate court rules. If you truly want to keep your final affairs private and you do not want the world to know about your estate plan, a living trust will keep your final distribution private. Your trust is not filed with the probate court and the only individuals that receive notice are named beneficiaries in the trust.
Goudy Bookletter 1911