he issue would become, they say, simply a matter of each private owner deciding who comes onto his privately owned property. They conclude their argument by saying that there would be no "open borders" in a system that is based entirely on private ownership of property.
Alas, such proponents are simply wrong. Even if every piece of government-owned property were privatized, the issue of government controlled borders versus open borders would still have to be confronted.
Suppose an American citizen owns a 20,000-acre ranch. It is one large contiguous tract of land. Half of the ranch is in Mexico and the other half is in the United States. Since he owns the entire ranch, the ranch owner does not have a fence dividing the ranch. He has roads throughout the ranch that enable him to travel freely throughout the ranch.
How does the ranch owner know when he crosses into Mexico and back into the United States? He doesn't.