Divided

Odyssey Book 20 line 188-190 Barry B Powell
Wikipedia Oikos (Adoption)
Odyssey Book 16 line 116-117 Barry B Powell
Wikipedia Oikos (Men)

A mixed herd of sheep and goats

But there is a problem.

.... strangers drive them off for themselves to eat, and they do not care for the son of the house. Nor do they tremble at the anger of the gods. They want to divide up the wealth of the king who is gone.

Odysseus' lifestock is in the proces to be divided over the strangers, meaning the suitors. They don't expect Odysseus to return, or if he does, to survive the confrontation with them. And apparantly they are supposed to take care of his son. There must have been some law or rule they should have followed.

An adopted son was no longer a member of his original oikos, but was transferred to the oikos of his adopter.

You see, if Telemachos gets adopted there will be no heir left since Telemachos was the only son of Odysseus and Odysseus was the only son of Laërtes and so on.

A man was the head (kyrios, κύριος) of the household. The kyrios was responsible for representing the interests of his oikos to the wider polis and providing legal protection to the women and minors with whom he shared his household.

It is to be expected that the Oikos (household) is falling in the hand of the Polis (City) in which the suitors have the majority. There the suitors will decide to divide the inheiritance among them. And Philiotios now said they already started dividing the herds.

Arkeisios fathered a single son, Laërtes, and he fathered Odysseus as his only son, and I was Odysseus' only child.

There are no brothers and there are no uncles, the family tree ends here. But the suitors do not want a maturing son, only a few years younger then themselfs taking their kingdom from them. So, they tryed to kill him anyhow.