(Reference: John Crook, Law and Life of Rome, Cornell University Press, c1967.)
In the agricultural society of the early Romans, the patriarchial farmer worked the land with his whole family, sons and slaves. The Roman "familia" included free members, those under various forms of guardianship and slaves. The rules regarding "filias familias" and "servus" were very much alike. The patriarchial power over life and death applied to both and neither could own anything. Both have only "peculium"- property legally belonging to the patriach that the son or slave was given for his own use. Further, family members under guardianship, (all freedmen who were minors and freedwomen,) could only alienate property with their guardian's consent. If you were in potestate you owned nothing. Whatever you acquired accrued automatically to your paterfamilias. You could make no gifts and if you borrowed money, it was a charge on your paterfamilias.
The authority of the patriarch lasted not merely until those in the familia grew up and formed their own conjugal groups, but until the day he died. Every member of the familia was in the potestas of the oldest surviving male ascendant or paterfamilias. His household jurisdiction dealt with offences of its members that threatened the family's reputation. He could inflict chastisements and even death, in judgment.
If the paterfamilias died, the familia would fall into the potestas of the next oldest ascendant in the male line. If there was none, those fee persons in the familia would become sui iuris.