The brewing paternity dispute involving U.S. model Anna Nicole Smith's new daughter now involves a sterile real estate mogul.

Real estate magnate Ted Thompson has signed an affidavit in which he claims that the former Playboy model attempted to convince him that he was her daughter's father -- despite the fact he had undergone a vasectomy in the past, said

Thompson alleges that after he turned down Smith, who he had an affair with last year, the 38-year-old actress eventually had her lawyer, Howard K. Stern, named as the official father of her new child.

In the affidavit, Thompson said Smith had confessed to him that the true father of Dannielynn Hope Marshall Stern was actually her former boyfriend, Larry Birkhead -- who has been fighting to be recognized as the father.

People magazine reported that Smith was released Monday from a Bahamas hospital where she had been treated for pneumonia for the last week.