We learn from Prisoner of Azkaban that Sirius Black was an unregistered animagus, and that his animagus form was a dog. Sirius Black was not the most mature of wizards, particularly when he was young. He was prone to playing pranks on Hogwarts students, which were sometimes even cruel, such as the prank on Severus Snape in the Shrieking Shack. 

***Is it possible that he mated with female dogs in his animagus form during his initial years?*** An ordinary dog might be extremely attracted to an animagus, due to *magic*.  If so, did he have any *canine* *heirs* running around? If he did, did he have a separate Will for them?

> Sirius’s will was discovered a week ago and that he left you
> everything he owned. You add a reasonable amount of gold to your
> account at gringotts, and you inherit all of Sirius’s personal
> possessions. Sirius also left you number twelve, Grimmauld Place.

Or, Dumbledore could have redacted some of the original Will to spare Harry the embarrassment, especially after Sirius' death. Note how Dumbledore tells Harry, instead of giving him a copy of the Will.