In order to gain ownership of previously unowned lands, you have to make use of them.
For example: a farmer homesteads property rights to a piece of land when he becomes the first to plow it and and plant it.
He cannot simply look at a piece of land and declare it his property, he has to be the original user.
Same applies to a mine shaft below the ground, somebody may have a farm 500 feet above you, but they did not homestead the soil 500 feet below them, you the miner have homesteaded it.
But also, consider if someone digging a tunnel under your house caused your house to collapse into it, they would be responsible for the damage as they have caused damage to your property, just as if a neighbors tree fell onto your house.
As for disputes of where your property extends too and where your neighbors property begins, private courts would be capable of solving these disputes.
Check out the Laissez-Faire Journal at LFJournal.com
"The State is a gang of thieves writ large." - Murray Rothbard
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