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Ok so, Satan is Diavolo's biological son and I won't take no for an answer.
When Lucifer and Diavolo first met they did the naked worm with each other. Unprotected. and when Lucifer cut his wings off that was the equivalent of birth, the real reason Diavolo gave them a free house is cause he wants to be a good baby daddy but Lucifer doesn't want him directly involved in their sons life.
Diavolo pays millions in child support.