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“This is like receiving the divorce papers for a couple that’s been separated for years,” he said.

AT&T’s purchase of fourth-ranked T-Mobile, announced in March, would have made it the largest cellphone company in the U.S. AT&T is now the second-largest wireless carrier, with more than 100 million subscribers, behind Verizon Wireless, with 108 million. Sprint has 53 million, followed by T-Mobile at 34 million.

T-Mobile endured without much investment from its parent company and without the highest-end devices such as Apple Inc.’s iPhone. It offered value packages to customers who brought phones from other carriers. Regulators feared the loss of T-Mobile as a competitor would hurt consumers.

AT&T will now have to pay Deutsche Telekom $3 billion in cash as a breakup fee and give it about $1 billion worth of airwaves, known as spectrum, that AT&T doesn’t need for the continued rollout of its high-speed “4G” network.

It will also enter into a roaming agreement with Deutsche Telekom so that AT&T’s and T-Mobile’s customers can use each other’s networks.

AT&T will take an accounting charge of $4 billion in the current quarter.

In pulling out, AT&T said the government’s attempts to block the deal do not change the challenges of the wireless phone industry. Cellphone companies have been clamoring for more airwaves to meet growing demand for faster downloads on smartphones and tablet computers.