MEXICO CITY—Three of Mexico's most prominent billionaires—who were once a cozy group of amigos protecting each other's backs—are now battling over how to divvy up the country's $35-billion-a-year telecommunication and TV-broadcast market.

The fight pits Carlos Slim, the world's richest man and principal owner of Mexico's biggest land-line and cellular-phone companies, against the country's top two media tycoons, Emilio Azcárraga, principal owner of No. 1 broadcaster Grupo Televisa SA B, and Ricardo Salinas, principal owner of TV Azteca SAB as well as the cellphone company Iusacell.

Mexico's economy is dominated by large companies that control their industries, and they rarely threaten each other by moving into other markets. But technological convergence has blurred the lines between the phone and TV industries, allowing both sides to invade each other's turf.

"The veneer of friendship is disappearing," says Eduardo Garcia, owner of Sentido Comun, an online business-news site in Mexico City. "Mexico's billionaires are battling over the prize using all the weapons at their disposal."

Key to the dispute is Mr. Slim's inability thus far to enter the TV market because of the terms under which he operates Telmex, the former state phone monopoly he bought in the early 1990s.