If you purchase a home from a taxable estate with another co-executor at appraised value rather than market to reduce additional estate tax how do you determine the third co-executor's fair portion?

The house must be included at fair market value as of the date of death regardless of the amount actually paid for the house. the only exception to this rule, would be if the executor elects the alternate valuation date, which would be the fair market value at the earlier of 6 months after date of death or the date ther property was sold.