Sean Avery, the controversial forward whose name could be found as often in tabloid gossip columns as on the sports pages during his season and a half with the Rangers, signed a four-year, $15.5 million contract with the Dallas Stars on Wednesday.

“It’s limitless what he can bring to us,” Brett Hull, the Stars’ co-general manager, said on a conference call. Hull added, “His skill level is getting better and better year by year, and that ability along with his grit, his toughness, his willingness to do anything to win, I just thought it was a no-brainer to have him in our lineup.”

The Rangers were busy during the second day of the N.H.L.’s free-agency period. They acquired two players, forwards Nikolai Zherdev and Dan Fritsche, from the Columbus Blue Jackets in a trade for defensemen Fedor Tyutin and Christian Backman.