The Rangers continued their promised roster overhaul just before the N.H.L. trade deadline on Monday, dealing the captain Ryan McDonagh and forward J. T. Miller to the Tampa Bay Lightning for three players and two draft picks.

McDonagh’s departure, which came a day after the Rangers traded forward Rick Nash to the Boston Bruins, completed for now a roster dismantling that the Rangers had warned their fans was coming. The Rangers last week dealt Nick Holden to the Bruins and sent Michael Grabner, their leading goal scorer, to the Devils, leaving them to move forward as a last-place team stripped of some of its most popular and reliable names with 19 games to go.

The Rangers signaled that big changes were coming two weeks ago in a letter from the team president, Glen Sather, and General Manager Jeff Gorton, telling fans that the team “may lose some familiar faces, guys we all care about and respect” in order to add young, skillful players.

In Monday’s deal, the Rangers acquired the 25-year-old Russian forward Vladislav Namestnikov and two prospects: Brett Howden and Libor Hajek. The Rangers also got Tampa Bay’s first-round pick in June’s draft and a conditional second-round draft pick in 2019, which will become a first-round selection if the Lightning, who lead the Atlantic Division, win the Stanley Cup this year or in 2019.

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