I prefer to start with Common Property as that is how early societies found the environment--shared by all, owned by no one. Of course this situation leads quickly to conflicts that call for Public Property and Private Property to manage the conflict. My guess is that bands or tribes claimed joint jurisdiction over some places, artifacts and tools. And within the band or tribe some individuals and family units further claimed jurisdiction over some places, artifacts and tools and even persons. These dynamics set the stage for social and legal systems to further define ownership limits, rights, and responsibilities that are changing even today. The main thing to keep in mind is that these distinctions and all the norms, morays, and laws are social constructions made be humans and changeable by humans. People often identify strongly with their property and are often willing to die for it.
Neighborhood ownership is an open question that needs social and political innovation. Weak neighborhoods (little ownership) weaken municipalities, counties, states, and nations--all of which are built of neighborhoods. Most importantly, weak neighborhoods cannot support their households and individuals.