The following is an excerpt from an email reply to a viewer question about the libertarian property concept:
So what is libertarianism? To understand libertarianism we must start with property. Property is a resource that can be said to be under the definite control of a single entity comprising individuals with agency. It is a norm that arises naturally from the link between individuated cognition (no such thing as a "collective brain") and scarcity (the condition of individuals have differing (subjective) and limitless designs on the same limited resource (objective)). Given an objective of minimizing violent conflict over said resource, conflict can be said to be minimized by definition when its use, possession, control and disposal are least disputed as proper to one entity vs. another. In this context, property can be described as more "private" the less ambiguity over control of the resource exists. At the extremes perfectly private property is where this entity completely controls it; no other entity does whatsoever and public property is where no one has any more control than anyone else.
Libertarianism is the consistent defense of property. Central to this defense is opposition to the State, defined as territorial monopoly on ultimate decision making. The term "monopoly" means an organization that can increase revenue by restricting output. This is possible only with the ability to violently suppress competition, which of course the State possesses in abundance. This is what makes it the ultimate decision maker. The problem here is that while it is the ultimate decision maker, it is not the only one with respect to property. You as a homeowner typically have a good deal of freedom in what you do with your house, for example, but stop paying property taxes and see how quickly that freedom vanishes. Everyone desires ultimate control of property and the only way to do this under the condition of a State (by definition) is to wrestle control of the State apparatus away from others with different designs. Resources that the State organization controls almost totally as well as ultimately are said to be "public" and those the State's control over is mostly "just" ultimate are said to be "private". Note that the colloquial definitions here closely correspond to the technical ones in the preceding paragraph. The State, therefore, is a massive engine of conflict over scarce resources and is by nature antithetical to the property norm.
The libertarian philosophy is highly delimited in scope (or "thin" as we call it). "Privatization" to a libertarian basically just means reducing criminality, especially working toward the abolition of protection rackets large and small; the State and the mafia respectively. "Private property" and "public property" in a Stateless society would not be very precise terms. It would be better to think of property with varying degrees of discrimination in admission. Low discrimination would be a community park. Medium discrimination would be a nightclub. High discrimination would be a personal abode. A community park might be owned individually or in trust or provided as a benefit by a business. What makes the arrangement libertarian is absence of violent coercion in its provision.
The State, as Murray Rothbard put it so well in Man, Economy and State is not an institution but a mode of behavior, i.e. monopolization by government. A government is an organization whose core function is the provision of legal and territorial protection. All governments in the world today act as States (Stately? Statishly?). Libertarianism's key insight is that this is not only not necessary, but necessarily suboptimal given property norms. The biggest misunderstanding of libertarians is that as such we oppose government. We do not (certainly not institutions of governance). We oppose monopoly. We favor a free market in everything, including government itself.