Jan yes, I'm sorry I didn't explain myself sufficiently. The terminology of 'donut hole' isn't one I'd thought of, but it's a good description. Examples that come to mind in the West have centered around water. A small rancher has a piece of property with a spring that his ancestors settled and gained title to. It's the only water within miles. He and his neighbors have worked out arrangements with each other including travel ways, access, sharing or selling water, etc and they've done so for decades.

Another more wealthy rancher wants that water, but the first won't sell--it's been in his family forever, he wants to leave it to his kids, he makes a living selling the water to others, etc. The second rancher buys up all the land around the first and using trespass, shuts off all access to the first, even for trips to town for shopping, etc. But more particularly to make the land worthless for selling the water or operating a small ranch business. (The reverse has also happened with flowing water, i.e. creeks being dammed, etc)

The first rancher has in fact just lost his land and it's extrinsic value. He's left with the options of abandonment or doing a forced sale to the second rancher at a drastically reduced price, who now has just increased the value of his own property multifold. Under the basis of pure trespass, the second rancher might be seen to have the right to do as he wants with his property and granting or denying access to his property. Courts in these cases have looked at the history of access for the property and ruled in favor of the first rancher. But they've ruled the other way against public access in a lot of the environmental/wilderness/wild animal passage vs public cases. Thus the Hague's and Bundy's in Nevada and eminent domain abuses in city/developer vs private owners. Even dozens of cases that are happening now for off-the-grid property owners vs public/private utility.