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.

“the iliad” (gr: “iliás”) is an epic poem by the ancient greek poet homer, which recounts some of the significant events of the final weeks of the trojan war and the greek siege of the city of troy (which was also known as ilion, ilios or ilium in ancient times).