Is it illegal to own a monopoly?

[rickinnocal]

No. Monopolies are perfectly legal, even under Sherman. What is illegal is using a monopoly or trust (A 'trust', in Sherman is what we would today typically call a cartel) to manipulate price and availability of a product or service.

The governments decision to break up AT&T, for example, was based not on the fact that it was a monopoly, but on the allegation that AT&T was using its monopoly position to artificially hike prices and keep prospective competitors out of the market.

Many US monopolies are "regulated monopolies". This means that the government uses the law to protect the monopoly from competition, and in return is allowed to control the monopolies pricing. In most places, for example, the garbage company is a regulated monopoly. The city does not allow homeowners to contract with anyone other than one specific company for garbage removal, and in exchange for that protection, the company needs city approval for rate hikes.

Richard