Google and the US government faced off in a federal court on Monday, as each side delivered closing arguments in a case revolving around the technology giant's alleged unfair domination of online advertising.

The trial in a Virginia federal court is Google's second US antitrust case now under way as the US government tries to rein in the power of big tech.

In a separate trial, a Washington judge ruled that Google's search business is an illegal monopoly, and the US Justice Department is asking that Google sell its Chrome browser business to resolve the case.

The latest case, also brought by the Justice Department, focuses on ad technology for the open web -- the complex system determining which online ads people see when they surf the internet.

The vast majority of websites use a trio of Google ad software products that together, leave no way for publishers to escape Google's advertising technology, the plaintiffs allege.

Publishers -- including News Corp and Gannett publishing --  complain that they are locked into Google's advertising technology in order to run ads on their websites.

"Google is once, twice, three times a monopolist," DOJ lawyer Aaron Teitelbaum told the court in closing arguments.

Presiding judge Leonie Brinkema has said that she would deliver her opinion swiftly, as early as next month.

Whatever Brinkema's judgment, the outcome will almost certainly be appealed, prolonging a process that could go all the way to the US Supreme Court.

The government alleges that Google controls the auction-style system that advertisers use to purchase advertising space online.

The US lawyers argue that this approach allows Google to charge higher prices to advertisers while sending less revenue to publishers such as news websites, many of which are struggling to stay in business.

The US argues that Google used its financial power to acquire potential rivals and corner the ad tech market, leaving advertisers and publishers with no choice but to use its technology.

The government wants Google to divest parts of its ad tech business.

Google dismissed the allegations as an attempt by the government to pick "winners and losers" in a diverse market.

The company argues that the display ads at issue are just a small share of today's ad tech business.

Google says the plaintiffs' definition of the market ignores ads that are also placed in search results, apps and social media platforms and where, taken as a whole, Google does not dominate.

"The law simply does not support what the plaintiffs are arguing in this case," said Google's lawyer Karen Dunn.

She warned that if Google were to lose the case, the winners would be rival tech giants such as Microsoft, Meta or Amazon, whose market share in online advertising is ascendant as Google's share is falling.

The DOJ countered that it simply "does not matter" that Google is competing in the broader market for online ads.

"That is a different question" than the market for ads on websites that is the target of the case, said Teitelbaum.

Google also points to US legal precedent, saying arguments similar to the government's have been refuted in previous antitrust cases.

Dunn also warned that forcing Google to work with rivals in its ad products would amount to government central planning that the court should reject.

If the judge finds Google to be at fault, a new phase of the trial would decide how the company should comply with that conclusion.

And all that could be moot if the incoming Trump administration decides to drop the case.

The president-elect has been a critic of Google's, but he warned earlier this month that breaking it up could be "a very dangerous thing."