User blog comment:Arachne sama/Shinigami Skills Heredity/@comment-5551986-20130614211615

I would only assume, members of the same family, have similar personalities (that being reflected on them, as in similar days, parents tend to raise their children how they were, although there are exceptions) this would lead me to believe they have slightly similar souls, which would be reflected slightly, on their zanpakuto or asauchi. Ever heard of the expression "like father, like son"?

Even so, I wouldn't assume Ichigo's zanpakuto be directly hereditary. His powers come from "White" who was being suppressed in Ichigo's mother by Isshin's shinigami powers, Ichigo being part Quincy may have absorbed his fathers and White reishi in some way, in how a foetus eats the food of its mother, maybe Ichigo absorbed her reiatsu, his fathers and whites, and incorporated White and his Fathers powers into one. Or White more or less just done something similar with Isshins powers.