What was the system by which branded cattle were allowed to graze freely on unfenced property?

The system by which branded cattle were allowed to graze freely on unfenced property was open range.

In the Western United States and Canada, open range refers ro rangeland where cattle roam freely regardless of land ownership. Where there are "open range" laws, those who aim to keep animals off their property must erect a fence to keep animals out; this also applies to public roads.

The Western open-range tradition emerged from the practice of unregulated grazing in newly acquired western lands.

whole lotta ptsd going on

the answer would be:

b. race