UPDATE 2-U.S. judge bars AIG bailout, bonuses from trial

* High-profile trial between AIG and ex-CEO opens

* Judge precludes talk of bonuses, investigations

* Ex-CEO Greenberg may testify as early as Tuesday (Adds quotes from opening statements)

By Lilla Zuill

NEW YORK, June 15 (Reuters) - The U.S. government bailout of AIG and controversial bonuses paid by the insurer cannot be brought up during the trial of the company's lawsuit involving former CEO Maurice "Hank" Greenberg, a judge ruled on Monday.

Instead, American International Group Inc's (AIG.N) case against Greenberg-controlled Starr International, will center on a large block of AIG shares held by Starr. The stock was worth $20 billion in 2005 when Greenberg was ousted from AIG, but tumbled in value as AIG shares dropped over the last year.

Starr, controlled by a group of trustees including Greenberg, and who were once AIG's senior management, ceased to be a compensation vehicle for AIG executives in 2005. It is now run by Greenberg as a private investment vehicle and for charity.

AIG, claiming breach of fiduciary duty, is seeking to wrest back shares held by Starr and the proceeds from any sales, at the same time as it tries to repay $85 billion in taxpayer bailout money.

AIG has said Starr International's share sales raised $4.3 billion, and it is seeking that amount as damages. The company also wants the remaining shares to hold in trust for future compensation.