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UPDATE 2-T-Mobile rolls out buyback plan after Sprint deal talks collapse

(Adds details on buyback from UBS conference, source comment on Deutsche Telekom's plans, share movement)

Dec 6 (Reuters) - T-Mobile US Inc said its board approved the U.S. wireless carrier's first-ever buyback program, a month after the company and rival Sprint Corp ended their deal talks.

Deutsche Telekom AG, which holds over 60 percent in T-Mobile, also plans to purchase additional shares, T-Mobile said on Wednesday.

The buyback of up to $1.5 billion of shares would start from Thursday and take place through Dec. 31, 2018, T-Mobile said.

"Coming off the Sprint deal with significant shareholder rotation happening, we think that we have a tremendous value here," CFO Braxton Carter said at the UBS Global Media and Communications Conference on Wednesday.

Combined with Deutsche Telekom's planned repurchases, the program could approach the $2 billion level, Carter said.

"(Deutsche Telekom) is finalizing plans right now," Carter said.

Through the buyback, Deutsche Telekom aims to hold its stake broadly steady, within a range of 1-2 percentage points, a source familiar with the matter told Reuters.

The issue of control was one of several deal-breakers in the T-Mobile-Sprint talks and the buyback would strengthen Deutsche Telekom's hand in any future merger talks.

Carter also said the company was focused on smaller, "tuck-in" acquisitions. "We think there's a lot of potential out there," he said. "That would be another use of cash."

T-Mobile's shares were up 1.3 percent at $61.73.

(Reporting by Laharee Chatterjee and Aishwarya Venugopal in Bengaluru, Anjali Athavaley in New York and Douglas Busvine in Frankfurt; Editing by Sriraj Kalluvila)