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Any assets that are distributed may incure a so called gift and generation skipping tax to the extent that they exceed 1,000,000. The estate may be eligible for an additional 1 million. But it is safe to assume that your estate will owe no gift tax based on the 1 million exclusion.
However, there is another issue of estate income tax. If the executor disposed of peroperty and liquidated assets before paying out the inheritance, then the estate would have had income, and a form 1041 needs to be filed.