They sign autographs.
No the Braves did
the Yankees. He was drafted by them.
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No. Barry Bonds has never signed with or played for the Yankees.
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C.C. Sabathia signed with the Yankees on December 18, 2008.
Mark Teixeira signed with the New York Yankees on December 23, 2008.
No. John Lackey signed with the Boston Red Sox.
Yes, the Yankees baseball team does have twitter. Their page is on there and you can check up on the Yankees just by following them!
Yankees
Of course, most baseball players will sign anything for a fan at the right moment.