Carmelo's history with George Karl dates all the way back to Melo's second season in the league when Karl became the Nuggets head coach. During their time together Carmelo established himself as the league's premier scorer and helped the Nuggets legitimize themselves as a real threat in the Western Conference.
The peak of their professional relationship happened in the 2008-09 season when the Nuggets made it all the way to the Western Conference Finals where they eventually lost to Kobe and his LA Lakers.
Two seasons later, the Nuggets went into the new season shrouded with trade rumors regarding their franchise player. It soon proved to be true that the trade became inevitable as Melo refused to sign his contract extension with the Nuggets and requested a trade.
In February 2011, Carmelo's wish to leave Denver finally came true as he was dealt with Chauncey Billups for Wilson Chandler, Danilo Gallinari, Timofey Mozgov, and a first-round pick in '14 along with swap right in '16.
In a recent Twitter post, former Nuggets head coach George Karl revealed that the trade which dealt Carmelo Anthony to New York was one of the best trades in NBA history.
In the first two years after the trade, the Nuggets made two first-round playoff appearances, and the Knicks made one first-round appearance and one trip to the semifinals. In the following three seasons, both teams didn't make the postseason, but the Nuggets had a better overall record - 99-147 vs the Knicks 86-160.
Denver wins this trade on the draft assets they acquired. The 2016 first-round pick swap they got from the Knicks turned out to be no.7 and they selected a guy that lit the bubble on fire - Jamal Murray. The 2014 first-round draft pick the Nuggets got from the Knicks was involved in a complex set of trades, and to spare you a headache - the Nuggets got Will Barton and Malik Beasly out of it.
Karl is right when he says that trade laid the foundation for the Denver Nuggets we know today. A lot of amazing front office work was involved as well (some of the wildest three and four team trades ever). At the time, everyone considered Denver a loser, but what we know now, they got the better part of the deal.