Taxpayer died in July with a Traditional IRA with basis.  However, the IRA was at three institutions.  At two of them, the beneficiaries were her children.  At the third, she did not name a beneficiary and it will end up in her estate.

I have spent a few hours researching this and I cannot find the answer.  I know the basis follows the IRA.  And if it was just split between three kids, I would allocate a third to each.    But that is not the case here.  When the beneficiaries are different at the various institutions holding the collective Traditional IRA, how do you allocate the basis? 

I was thinking of trying to somehow determine the value held by each institution at the date of death, and then allocating the basis by the percentage each institution held to the overall value at date of death.  Once I have that, I can then determine how much goes to each beneficiary, including the estate.

Does that seem reasonable?  Or is there some rule covering this that I am oblivious to?