Players and teams could begin negotiating just past midnight EDT on Tuesday morning, though contracts can't be signed until July 10, after next season's salary cap has been set.
Though many expect that trio to stay with the Heat, Anthony could be persuaded to leave the New York Knicks for a team he believes gives him a better chance to compete for a championship. He was visiting Chicago on Tuesday, and Houston and Dallas also could try to pry the 2012-13 scoring champion away from the Knicks, who can pay him around $30 million more than any team under NBA rules.
Longtime stars Paul Pierce, Dirk Nowitzki and Pau Gasol also are free agents, along with players such as Toronto's Kyle Lowry and Indiana's Lance Stephenson, who are coming off their best seasons in the league.
It's the most anticipated free agency class since 2010, when James led a class that included Wade, Bosh, and other All-Stars such as Amare Stoudemire and Joe Johnson.
That free agency period changed the NBA. This one might mostly change the Heat.
They are in need of an upgrade after getting smashed by San Antonio in the finals, and the Big Three could help give them the means to make one if they agree to salaries that won't clog up too much of the cap.
Knicks president Phil Jackson hopes Anthony also agrees to take less than a maximum salary, which would be more than $125 million if he stayed in New York.
Also in New York, the Brooklyn Nets stagger into free agency without their coach after letting Jason Kidd leave for the Milwaukee Bucks. The teams agreed to a deal Monday, with the Bucks sending two future second-round picks to the Nets, who allowed Kidd to pursue other jobs after denying his request for more power in the organization.
Brooklyn has Pierce and Shaun Livingston among its key players who are free agents.
The Los Angeles Lakers have plenty of money to offer, along with the chance to play with Kobe Bryant. Teams such as Phoenix and Atlanta have some good pieces in place and enough cap space to add another.
They would love a shot at James, as would his home state Cleveland Cavaliers, the team he left in 2010. But it's unclear how seriously the four-time MVP will listen to other teams after meeting with six suitors when he was last a free agent.
The Cavaliers may not get James back, but they will have their current All-Star for a while. Owner Dan Gilbert wrote on Twitter early Tuesday morning that he had an agreement on a five-year contract extension with Kyrie Irving, the No. 1 pick in the 2011 draft.
''Looking forward to the next 6 years of Kyrie Irving in CLE. Just shook hands & intend to sign on the 10th,'' Gilbert wrote, adding that he couldn't be more excited about the Cavs' future.
Players such as Cleveland's Luol Deng and Washington's Trevor Ariza could be good fallback options for teams who can't get James or Anthony.