For anyone that read the previous chapter and complaint about it not being realistic or stupid, let us go over a few things.
This is a fanfic n a world of magic, goblins, dragons, and near-immortals, it's not meant to be realistic.
For anyone that thinks that Arcturus wouldn't hand over his house and power that easily, let us see.
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In Canon, Arcturus dies roughly the same year Harry Potter first attends Hogwarts.
The Black Family are patriarchal, meaning they don't have female leaders and always a=have a male head, and since he was dying, that title would have been given to Lucius Malfoy until our MC became fifteen.
Arcturus was a smart, cunning, respected, and feared individual, he was nothing like the pompous and arrogant Lucius, so i personally think he would hate Lucius or at least resent the man.
So he made the decision to make our MC the head of the family knowing Walburga will be around for a little while to keep him company and give him advice.