No, the remaining cash that is distributed is not income, it's an inheritance and not subject to federal tax. There are a handful of states that tax the receipt of inheritances, but California isn't one of them.
If any of the surviving children live in a state with an inheritance tax, they should check the applicable state rules to ensure the total amount of their inheritance (other items in addition to this cash, if applicable) don't subject them to state tax. The states to check include Iowa, Kentucky, Maryland, Nebraska, New Jersey, and Pennsylvania.
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