Kirilenko spent 10 seasons with the Utah Jazz where he went from playing alongside Hall of Famer John Stockton and Karl Malone to being a focal point of the team due to his all-around game.
After his multiyear contract with the Jazz ended, Kirilenko became an unrestricted free agent and due to the uncertainty of the lockout, signed a contract with CSKA Moscow with an NBA out, giving him more options if he wanted to return (since there is going to be a 2011-12 NBA season).
The Utah Jazz are looking to rebuild around young big men Derrick Favors and Enes Kanter while Kirilenko was looking to join a possible contender at this stage of his NBA career.
Joining the New Jersey Nets would allow Kirilenko to once again play alongside point guard Deron Williams (who spent five-and-a-half years in Utah) and may also help the team show Deron Williams that they want him to be a member of the team long-term.
The Sacramento Kings are looking for a veteran to play alongside DeMarcus Cousins and Tyreke Evans that can also be an influence to the younger players on the team.
It remains to be seen what Kirilenko will do and it is likely that he does make a return to the NBA on a shorter contract basis and he can be a contributor with his all-around abilities.