There are a variety of manifestations of intellectual property - trademarks, copyrights, patents. Many things can be copyrighted and patented ... even business methods can be copyrighted! Famously, Amazon patented its so-called "1-click" purchase option, threatening other online sellers who dared to imitate its brilliant invention with lawsuits!
Leaving aside conceptual definitions of IP, what are its ultimate effects? The ultimate effects of IP are to prohibit certain sorts of actions by individuals which are construed to be violations of the "intellectual property" rights of others.
Now, the essence of property - in a Hoppean/Rothbardian conception - is to assign rights to exclusive use of a physical resource to a specific individual. If John owns a car, that means John has the exclusive right to operate and control the car and to determine who else is allowed to operate and control the car. When the State arrogates to itself the authority to license John's operation of his own property, the State is actually aggressing against John by infringing on the exclusivity of John's rights to operate and control his car.
But does this mean John is free to do anything he likes with his car, lest we commit the unpardonable sin of aggressing against John's all-hallowed "liberty"? No - if John uses his property in such a way that it interferes with the exclusive rights of another individual to control their own property, John is aggressing against that individual and they, thereby, have justification for the use of force against John to prevent him from using his property in that way (or taking him to court to seek retaliation against him). But the State, in licensing (or not) John's use of his own property is not suffering from any interference on John's part. If John refuses to be licensed, this does not harm any State property or anyone else's property, for that matter. The dispute between the State and John - regarding licensure of the use of his vehicle - is completely gratuitous. Gratuitous disputes can and will arise even in the absence of an aggressive State but those who initiate such gratuitous disputes at least have to bear the costs of their decision to harass a peaceful citizen. Gratuitous disputes which are subsidized by the State, on the other hand, pass the costs off onto the taxpayer - explaining why gratuitous disputes (e.g. victimless crimes) are far more numerous than disputes originating from property conflicts.
Intellectual property, in my opinion, is a form of gratuitous dispute. I say "in my opinion" because it's impossible to know in the absence of a market in law. The only way to know for sure is to have a free market in law. In a free market of law, I believe that the costs of pursuing such gratuitous disputes would swamp any possible benefits which could be garnered. It is only the subsidization of intellectual property claimants* by the State that makes such enterprises profitable. If a musical band recorded themselves in a studio to CD and released the CD in a stateless society, who would combat the "pirating" of the band's CD once they released it to the public? In each case, they would have to bring individual lawsuits against every individual who they deem to have "illegally" copied their IP. Such legal action would be prohibitively expensive (witness the RIAA's losing battle to legally intimidate people into not copying songs... and that with the aid of State subsidy!) One could take a Coasean approach and say that this, in itself, proves that IP should not be considered property but something deeper is at stake and that is that all property rights consist of rights to exclusive control of scarce physical resources for the purpose of avoiding conflicts. Expanding the definition of property to include intangibles - such as numbers, images, patterns, business methods, and so on, results in the multiplication of conflicts.
Gratuitous conflicts are the essence of State-delegated authority - look at the number of persons filling our prisons for "crimes" related to the possession, distribution and consumption of marijuana or other drugs. Whenever the State issues and enforces statutory or regulatory dictates - "Thou shalt ____" or "Thou shalt not ___" - it is creating gratuitous conflict. This is why I say that intellectual property is the essence of the State's self-delegated authority. Ordering people around like they are slaves is what the State does and intellectual property is just one example, among millions, of this.
In a competitive law society, we would expect that only those conflicts which it is profitable to prosecute would be prosecuted. A family seeking retaliation against a murdered family member will pay the costs (or their crime-insurance agency will) needed to convict the perpetrator, making such prosecution profitable. Victims of theft or assault will be able to profitably sell claims to repossession and retribution against their aggressor to for-profit bounty/repo businesses. But the reason that these things can be profitably done is exactly because they concern the allocation of scarce resources. Just like nobody can profitably sell air, so no one could profitably prosecute violations of perceived IP.
Finally, it is conceivable that societies of individuals who value ultra-high-quality media - and are willing to pay for the privilege to consume it - could develop. For example, perhaps you could have an enclave of blockbuster movie addicts who live in the Hollywood area and, as part of the contractual agreement to owning property in that region, they agree to abide by what is essentially IP law. Tourists might travel to the territory - a "Las Vegas for blockbuster buffs" - to get a taste of the rich media experiences which can only exist in a territory with ironclad IP rights. This would not be unlike other enclave communities that would likely develop around cult religions, anachronistic religions or tribal economics, such as the FLDS, Amish or anarcho-communes. There is nothing inherently anti-liberal about this, so long as these enclaves do not become aggressive and attempt to export the costs of their irrational social structures onto individuals living outside their territory. But it is highly unlikely, in my opinion, that international private law would ever recognize and enforce such bizarre legal rules.
*For example, the FBI warning regarding piracy at the opening of every Hollywood movie - who pays for the vigorous investigation and prosecution of piracy by the FBI? Not Hollywood... we do!