As for what I have understood, libertarians (or the "most liberal" stand-point, whatever the correct term is) wants a free market, press, liberty for all, etc. and a small government. That means, as I´ve understood, that everybody, in all circumstances are free to act as they want within the boundaries of the law which is supervised by the as small government as possible. To me this seem to introduce a paradox since as once a company become very large it will begin to act as a "government" and will effect our lives but on the other hand they should be able to act as they want. What is the libertarians view upon this?
The following is a synopsis and explanation of common beliefs the Libertarian free market philosophy. It is important to understand that Libertarianism is made up of individual philosophies so while I believe this synopsizes the majority's opinion there are certainly discrepancies among individual beliefs, and I am sure some individual Libertarians that disagree with most of this. Libertarianism is primarily about individual freedom, and for many that is far more important than a working economic model.
Large companies with near monopolies are actually enabled through regulations and protections provided by the government. Regulations on how things must be built to meet standards set by the government make entry into the marketplace cost prohibitive to many entrepreneurs. This allows big businesses to simply acquire the very few that decide to enter the market. If you remove this regulation and protectionism, as the libertarian position espouses, the cost of entry is reduced significantly. You get more entries into the marketplace, to many for any few companies to acquire, especially since the majority will fail. This gives more chances for real innovation and competition that allows a small company to grow and become a real competitor in the marketplace.
Another barrier to competition is patents. In a true free market the only protection a company would get to its innovation would be the time from when it is conceived to the time where its competitors find out and adapt their products to take advantage of the innovation. A company could catch up in the market in just the amount of time it takes to reverse engineer and implement it in their own product. This would have the effect that there would be a more diverse selection of products and lowered profit margins which would prevent companies from growing as large as they can today with these protections.
The fact that the artificial controls are removed would make it much harder for a company to grow large and stay successful. This dynamic actually tends to benefit the small specialized company over the large conglomerate.
There are certainly downsides to this market. Quality among a diverse and unregulated group of producers will vary greatly. In this market products that are unsafe are likely to find their way into consumer hands and cause harm at a greater rate than today. Without the regulation there would likely be a greater incidence of misrepresentation of products as well. Testing of medicines and procedures is going to be less costly in terms of money, but the efficacy and safety of these products are going to be less certain, and likely unknown to the average person.
Large corporations do not "act as governments" in the Weberian sense of enforcing a monopoly on the legitimate use of violence.
Governments assert full authority within their jurisdiction, so aside from a few exceptions like customary diplomatic immunity, everybody in the jurisdiction will be subject to governmental authority. It's generally unlikely that a corporation will push into the realm of using a police force or court system to enforce rules against non-customers and non-employees.
One may choose to interact with a company or not (though in some cases there may be a limited range of alternatives). That relationship is generally not present with governments, who generally reserve to themselves the power to decide when to enforce rules and decrees upon residents. That's the most fundamental distinction between governments and non-governments, and that's why it's unlikely for a corporation to simply cross over into controlling the behavior of all residents of a geographic area, without their consent.
Even the largest corporations (e.g., Walmart) are subject to competition, which is a key component of the libertarian philosophy. It is competition which guarantees that corporations do not take advantage of any situation. In the case of Walmart, it has customers to account to; if they do not behave in a competitive manner, they will suffer from declining profits.
There is competition even for Walmart (and anyone who is looking can see that Amazon.com is a huge threat to Walmart if it doesn't learn to compete against them).
Libertarians generally believe that markets are the most efficient allocator of resources in almost all circumstances (there are a few exceptions). The question is one of arms-length transactions in which no one is forced to engage in a given transaction.
Corporations exist at the prerogative of government, and thus cannot behave in a a manner that is contrary to the law. Since government creates its own law, government always operates at an advantage, so there is a fundamental difference between a corporation and a government that can never be eliminated.
At the moment your question does not show any understanding of libertarian theory. In particular, there are two notions that are very vague in your question:
- The notion that a big company somehow starts to "act as a government"; and
- The notion that libertarians let people "act as they want".
The latter is completely false - libertarianism clearly precludes a wide range of behaviours (e.g., murder, aggression, etc.) even if a person wants to engage in these behaviours. The former is also false - to the extent that libertarianism allows any government prerogatives (which depends on the particular branch of libertarianism) these are still powers exclusively for the government. It is unclear how you envision a big company starting to act like a government.