Telefonica says it has achieved part of its goal. Cellphone use has quadrupled since the company arrived, it says, and it has helped put handsets into the hands of rural peasants and street vendors while shrinking the cost of service.

But from a business perspective, Telefonica has spent a fortune in Mexico while remaining a low-end brand. And in struggling to reach solid ground, it has run into regulatory trouble.

The company's $13 billion investment in Movistar, the Mexico unit, has won it 22 percent of mobile phone lines in the country, yet it gets only 12 percent of what Mexicans spend on such service. High-end rival Nextel has the same share of mobile spending with only 4 percent of phone lines.

Telefonica does not disclose its net profit for Mexico, and a spokeswoman declined to provide figures. What is clear, analysts say, is that the company performs poorly, given what it spends in Latin America's second-biggest economy.

In 2010, the year Telefonica invested in its 3G network, the Mexico unit reported operating income of about a third of the roughly $2.1 billion invested.

Last year was not much better. Operating income sank 8 percent, and the company curtailed investment.

While investors shake their heads, regulators are giving Telefonica a closer look.

In late January, a federal court ordered the country's competition watchdog to investigate ties between Telefonica and Slim's businesses.

Telefonica rivals raised flags after the company broke with the rest of the industry in late 2010 and agreed to pay Slim much more to tap his vast phone network than other phone operators were willing to pay.

That sudden, accommodating attitude towards Slim smacks of collusion, rivals say.

"We have long sought an investigation that will allow healthy and fair competition in the phone market," said an official with Televisa, the country's top television broadcaster, which asked for the Telefonica probe.

Telefonica and Slim deny the charges and insist that they compete throughout Latin America.

Analysts say it is odd that Telefonica agreed to pay higher interconnection rates, the toll a phone company charges for access to its network.

Telefonica executives say they have an awkward explanation: While low interconnection tariffs would let it challenge Slim with better service or phone gadgets, the company relies on the connection fees that other phone users pay to reach their poorer clients.

So while the company hopes to one day lure the wealthy with low rates, it cannot yet forgo the revenue it gets from calls made to its dial-shy customers.

"The market conditions have changed and we need to adapt," said a Telefonica executive who requested anonymity to speak openly about company strategy.

That dilemma - keeping low-end clients while chasing more affluent users - has defined Telefonica's recent years in Mexico.

AWKWARD TRANSITION

Telefonica's revenue in Mexico dropped 15 percent last year, and executives acknowledge that pressure from investors to sell their Mexico stake could increase without a quick turnaround.

Ten years ago, the Mexico market looked like a good bet for Telefonica.

Few Mexicans had cell phones, and those who did were paying dearly for them. Telefonica, with deep pockets, was going to bring mobile services to the masses.

Francisco Gil, the Telefonica chief in Mexico and a former Mexican finance minister, waged an open battle to win the hearts and minds of the public and regulators.

Telmex, Slim's home phone company, is "a state within a state," Gil said in 2008, and "a monopoly with a sense of humor" for insisting that it faced real competition.

Telefonica had a simple strategy in Mexico: Appeal to the poor as it climbed into wealthier ends of the market and challenged Slim at every turn.

But Telefonica was playing catch-up with Slim, who privatized state-owned Telmex at the end of 1990 and pioneered the country's mobile market a few years later.

Slim had home field advantage and years running a profitable, de facto monopoly in Mexico before the market was opened to competition.

By the time Telefonica arrived, Slim had already proved that he had the wealth and regulatory clout to defend his turf against foreign interlopers.

MCI, later acquired by Verizon, folded Avantel, its Mexican long-distance operation in 2006, a decade after forming it.

In 2003, Verizon and Vodafone left Mexico after a roughly two-year partnership and more than $1 billion spent trying to beef up mobile carrier Iusacell, which they handed off to local media mogul Ricardo Salinas instead of facing bankruptcy.

Analysts say Telefonica underestimated the grinding battle they would face against Slim.

"Speaking from experience, fighting Slim is trench warfare," said Carlos Escalante, an independent consultant who previously worked at Slim home phone rival Axtel.

As it scrambled for market share, Telefonica had to wage costly battles with Slim, regulators and other rivals.

COMPETING WITH A TITAN

Telefonica saw no way to avoid a war of attrition and decided to go after the most accessible end of the market.

"We arrived in Mexico later than others," said the Telefonica executive. "It was easier to gain customers on the lower part of the pyramid."

The company recruited Gil, a veteran Slim-fighter from his time as head of Avantel, to lead Telefonica as it built a network and tried to persuade clients and regulators.

In one instance, the company fought for and helped win the right of customers to transfer their Slim cellphone numbers to rival operators, and Telefonica for years fought alongside other Slim rivals for lower interconnection rates.

Within Telefonica, anxiety increased as executives realized that customers who pay for their service in small bills could not justify the company's aggressive spending.

Serving the low end of the phone market, always a business of narrow margins, was doubly risky because it relied on income from interconnection rates, which are drifting down in markets around the globe.

At some point, executives knew, Telefonica would have to shift focus to high-end customers.

Executives say the moment for transition has come, but with terrible timing.

As Telefonica's home business in Spain labors under a heavy debt load, investors are impatient for a quick turnaround in Mexico.

Movistar is trying to address these worries now.

For starters, Telefonica has said it will drop its backing of the national football team and get behind events that attract well-heeled clients.

This is not the first time the company has tried to convince investors it can change its fortunes in Mexico.

A year ago, Jose Maria Alvarez Pallete, then Telefonica's chief executive officer in Latin America, said: "We think we have everything needed not only to turn around the situation (but) become ... a real challenger in Mexico."

In September, Alvarez Pallete was replaced as part of a broad management reshuffle.

(Reporting by Patrick Rucker and Elinor Comlay; Additional reporting by Isabella Cota and Tomas Sarmiento; Editing by Martin Howell and Prudence Crowther)

By Patrick Rucker and Elinor Comlay