User blog comment:Arachne sama/Shinigami Skills Heredity/@comment-8295743-20130615003956

Well, I think it's safe to assume that Shinigami powers can indeed be hereditary, but not guaranteed. Obvious examples are Ichigo and Isshin, along with Byakuya and his family. The Shiba Clan is proof that not all members of a family will inherit Shinigami abilities, although it can be argued Kukkaku and her siblings have the potential, but chose not to. We've seen that Kukakku can use Kido spells, and we know that Kaien was quite strong. Every member of the Kuchiki Clan that's been mentioned was a Shinigami, and we know that apart from Soi Fon, the Onmituskido has always been led by the head of the Shihoin Clan. A less known example is Tetsuzamon, whose mother was the former lieutenant of Squad Three under Rose.

My theory on the zanpakto of Ginrei being so similiar to Byakuya is simple: It was less work for the animators(Is his sword seen in color or in great detail in the manga? I can't remember). I have no theories on Engetsu and Zangetsu, especially since we have discovered what Zangetsu really was.