CalPERS, the giant California state pension fund, is taking a close look at its investment with Ralph Whitworth, who heads Relational Investors, a shareholder activist firm based in San Diego.

A law firm hired by CalPERS is examining the nearly $17 million Relational paid an obscure middleman who helped secure business from the pension fund, The Wall Street Journal reports today.

Relational Investors is headed by Ralph V. Whitworth and David Batchelder, who met while working in the 1980s for Texas oilman and corporate raider T. Boone Pickens.

Relational buys up stakes in underperforming companies like Mattel and J.C. Penney for a turnaround directed by Whitworth.

CalPERS is Relational’s biggest investor. The pension fund has about $1.5 billion in Relational.

Huge fees are standard for middlemen who successfully line up investments from CalPERS, but Relational’s payment to Tullig Inc. stands out. No one earned more from a single client.

Tullig Inc. is an obscure New York firm headed by an obscure man named Donal Murphy. What he did to earn his rich paycheck is as clear as mud.

Essentially, these middlemen are lobbyists and operators. It’s a shady business — money buying more money — that is finally getting some attention following a massive kickback and bribery scheme at New York State’s public pension fund.

Whitworth is perhaps best known for paying Paul McCartney $1 million in 2003 to perform at his wife’s private birthday party at a restaurant Rancho Santa Fe. The couple filed for divorce less than a year later.