Each owner in a community grant held private ownership of what?

In the system of community grants in New Mexico, each owner had private ownership rights over their individual homes and, typically, only the small plot of land immediately associated with those homes, such as gardens or small agriculture areas. This system often emphasized individual ownership of plots while maintaining communal governance and shared responsibilities for larger community lands. Hence, the correct answer reflects that ownership was limited to the specific plot designated to the household, affirming the focus on personal property rights within a cooperative structure.

The other options suggest broader ownership than what the community grant system entailed. For instance, the idea of owning a fraction share of all other community land implies a level of ownership beyond individual plots, which is not characteristic of this system. Similarly, suggesting ownership of enough land for many future generations misrepresents the limited size and scope of individual plots in a community grant. Thus, focusing solely on the individual plot and gardens aligns accurately with historical understandings of community grants in New Mexico.