SAN FRANCISCO – With billions of dollars and control of the U.S. smartphone and computer tablets markets at stake, jury selection began Monday in a closely watched trial between two of the world’s leading tech companies over patents.

Apple Inc. filed a lawsuit against Samsung Electronics Co. last year alleging the world’s largest technology company’s smartphones and computer tablets are illegal knockoffs of its popular iPhone and iPad products.

Cupertino-based Apple is demanding $2.5 billion in damages, an award that would dwarf the largest patent-related verdict to date.

Samsung countered that Apple is doing the stealing and that some of the technology at issue — such as the rounded rectangular designs of smartphones and tablets — has long been standard in the industry.

The case is just the latest skirmish between the two companies over product designs.

A similar trial began last week, and the two companies have been fighting in courts in the United Kingdom and Germany.

Industrywide, some 50 lawsuits have been filed by myriad telecommunications companies jockeying for position in the burgeoning $219 billion market for smartphones and computer tablets.

U.S. District Judge Lucy Koh in San Jose last month ordered Samsung to pull its Galaxy 10.1 computer tablet from the U.S. market pending the outcome of the upcoming trial, though the judge barred Apple attorneys from telling jurors about the ban.

In some sense the big part of the case is not Apple’s demands for damages but whether Samsung gets to sell its products,” said Mark A. Lemley, a Stanford Law School professor.

Lemley said a verdict in Apple’s favor could send a message to consumers that Android-based products such as Samsung’s are in legal jeopardy.

A verdict in Samsung’s favor could lead to higher-priced Apple products.