I see that Autolykos has responded, but I have a few things to say too. The question is not “Did someone abandon his property?” The question “What are the criteria for abandoning property?”
One way to abandon your property would be to sign a legal document, have it notarized, publish an ad in the paper, put out a commercial, and staple your legal document to your property. This would be a very obvious way to make it clear to everyone that it can be homesteaded. Maybe that is practical for very valuable pieces of property, such as land or an airplane, but must we really do this for everything? Of course not.
Consider trash. Trash is property that you are abandoning. How often do you sign and notarize documents saying that you are abandoning your trash? I can’t recall a time I’ve ever done that, and as far as I’m aware, I don’t know anyone who has ever done that. There is a custom regarding trash, at least in America, though I wouldn’t be surprised if it were more or less universal. In America, when we put our property in a dumpster or on the side of a road, we are signalling to the community that we are abandoning this property. It is trash and can be homesteaded. Most of the time, this trash just gets taken to the dump. But sometimes people abandon sofas or television sets, and people end up claiming and homesteading these things.
So, the question is, as Autolykos pointed out, what constitutes abandonment? Surely no one needs to staple a notarized document saying that the trash on the side of the road is abandoned? There is a custom already for this purpose. So, the question is, what constitutes abandoning land? As I pointed out, in the case of expensive and valuable property, the customs regarding abandonment would probably be much stricter. But there is no objective reason why someone can’t abandon their property without formally saying so.
Consider marriage. A couple can have a ceremony and sign some documents stating that they are married. Or they can live together for X number of years and have what is called a “common law marriage”. Certainly they are married in either scenario. Making a formal statement only speeds the process up and makes it more obvious to the community. But a common law marriage is still a marriage.
Needless to say, I completely disagree. Is it heinous that many stores have security cameras? Of course not. They have the security cameras there for security. If you steal or otherwise disrupt the store, they will use those cameras as evidence and throw you out and maybe even press charges.
It is the same with private roads. If you want to continue to drive on these private roads, you have to pay a fee for speeding. Otherwise, go find another road to drive on. It’s a private road, and you don’t have a right to it.
You’ve missed the point completely. I suggest that you read What Law Is and A Praxeological Account of Law by forum member Clayton.