Tamamo Cat > Tamamo > Suzuka

the way i understood how it worked is that Daji got split among all the Tamamos so technically all of them are Daji but Daji also effectively ceased to exist as an entity since there so little of her in each Tail. And the one that got the "biggest" slice of the Daji pie was Cat as a way to show how little of Daji remained since Cat is wholesome unlike base Tamamo

how wrong was i?