Updates throughout

April 17 (Reuters) - Alphabet's GOOGL.O Google illegally dominated two markets for online advertising technology, a federal judge said on Thursday, dealing another blow to the tech titan in an antitrust case brought by the U.S.

The ruling could allow prosecutors to argue for a breakup of Google's advertising products. The internet search giant now faces the possibility of two different U.S. courts ordering it to sell assets or change its business practices.

A judge in Washington will hold a trial next week on the Department of Justice's request to make Google sell its Chrome browser and take other measures to end its dominance in online search.

Here is a look at the U.S. antitrust cases that have Google playing defense and that could help shape the company's future.

DIGITAL ADVERTISING

U.S. District Judge Leonie Brinkema in Alexandria, Virginia, ruled on Thursday that Google unlawfully monopolized markets for publisher ad servers and the market for ad exchanges, which sit between buyers and sellers. Antitrust enforcers failed to show the company had a monopoly in advertiser ad networks, she wrote.

The decision paves the way for prosecutors to push for a breakup of Google's ad tech business. The U.S. Department of Justice has said Google should have to sell off at least its Google Ad Manager, which includes the company's publisher ad server and its ad exchange.

Google has previously explored selling off its ad exchange to appease European antitrust regulators, Reuters reported in September.

ONLINE SEARCH

Google's dominance over online search is the centerpiece of a lawsuit filed by the Justice Department in federal court in Washington in 2020. After a ruling in August that Google illegally monopolized the search market, U.S. Department of Justice prosecutors argued last November that the company must sell Chrome, share data and search results with rivals and possibly sell its Android smartphone software.

Their proposals include ending exclusive agreements in which Google pays billions of dollars annually to Apple and other device vendors to make its search engine the default on their tablets and smartphones.

Google has called the proposals staggering. Some experts have also said the efforts by U.S. antitrust regulators were likely to run into legal challenges on grounds that the remedies were extreme.

In December, Google proposed a loosening of its agreements with Apple AAPL.O and others to set Google as the default search engine on new devices, in a bid to address a U.S. ruling that it unlawfully dominates online search.

U.S. District Judge Amit Mehta has scheduled a trial on the proposals for April, although President Donald Trump and the DOJ's next antitrust head could step in and change course in the case.

ANDROID APPS

U.S. District Judge James Donato in San Francisco had ordered Google to overhaul parts of its Android app business in October last year. For three years beginning in November, Google under the order must allow Android users to download rival app platforms and use competing in-app payment methods, and it cannot pay device makers to preinstall its app store Play.

Google asked a U.S. appeals court in California in February this year to overturn the October app store verdict, saying that the trial judge made legal errors in the antitrust case that unfairly benefited "Fortnite" maker Epic Games.

Google, in a related Play case, said it will pay $700 million to resolve claims by consumers and U.S. states that it charged inflated prices for apps. That proposed settlement is pending before Donato, who has questioned whether the amount is sufficient.

Separately, Epic had brought a new lawsuit in September, accusing Google of unlawfully conspiring with device maker Samsung to protect Play from competition. Samsung and Google denied the claims.

(Compiled by Mike Scarcella in Washington and Juby Babu in Mexico City; Editing by David Bario, Will Dunham and Pooja Desai)

((Mike.Scarcella@thomsonreuters.com;))