The original household would have to sell the secondary properties first, back to the town, so the ones splitting off can purchase them anew.
If you also had NRaas StoryProgression and the SP Money module, then there would be the option of the original household retaining ownership of the secondary lots and becoming the landlords of the ones splitting off and moving into them, who would then become tenants and pay rent plus only a fraction of the property taxes with the usual twice weekly bills. But that option does not exist without the mod.