The university's lawyers told the panel of six women and six men that Fawcett repeatedly described herself as the portrait's owner before her death in 2009, and her dying wishes included that all her artwork be given to the school.
O'Neal's lawyer said, however, that the university is relying on witnesses who had animosity toward the Oscar-nominated actor and evidence would show the disputed artwork was a gift to O'Neal from Warhol.
Warhol created two portraits of Fawcett for a television special in 1980. They are currently separated by thousands of miles, with one hanging in a museum at Fawcett's alma mater and the other on display in O'Neal's beachside home.
David Beck, an attorney for the university, told jurors that O'Neal took the disputed portrait from Fawcett's home after her death and should have to give it to the school.
Beck noted that Fawcett had both portraits hanging in her condominium when she died after a lengthy battle with cancer in June 2009.
"One of them was hanging in her living room and one at the entrance to her bedroom on the day of her death," Beck said.
O'Neal's lawyer Marty Singer rejected the university's characterization of O'Neal's actions, saying the actor had permission to take the portrait from Fawcett's home.
O'Neal contends he introduced Warhol to Fawcett and requested that he receive one of the artist's portraits of the model and "Charlie's Angels" star.
Warhol gave Fawcett and O'Neal several pieces of art during his lifetime, Singer said, including a napkin drawing that the actor says the university should return to him.
"Apparently for this university, one iconic Warhol portrait is not enough," Singer said.
Beck showed jurors Fawcett's living trust and told the panel that the actress chose not to leave anything to O'Neal. There's evidence that Fawcett described both of the portraits as her own, Beck said.
"We are now told, since Farrah is now dead and can't speak for herself, and Andy Warhol is dead and can't speak for himself, Mr. O'Neal says that portrait was never Farrah's to begin with," Beck said.
Warhol created the two portraits in 1980 from Polaroid pictures he shot of Fawcett for a television special aired by "20/20". The two portraits were slightly different and meant to be displayed side-by-side, Beck said. He showed the jury a picture of Fawcett with both images in the background, one which had her hair colored in, the other one colorless except for her eyes and lips.
The university wants to make sure the portraits are available for viewing by the public at its Blanton Museum of Art, Beck said.
Singer attacked the university's witnesses, saying the school was relying on two people who dislike O'Neal - a former collaborator who has sued the actor three times, and one of the actress's ex-boyfriends.
Beck told jurors they could evaluate the credibility of all witnesses and told the panel that he would present some of O'Neal's entries from his journal. The actor didn't mention Warhol agreeing to give him one of the portraits, the lawyer said.
O'Neal has said he intends to give the artwork to his son, Redmond. Redmond O'Neal is the only son between the actor and Fawcett.
Redmond O'Neal, 28, who has accompanied his father to court throughout jury selection and days of pretrial motions, will not be able to sit in on the trial until after he testifies, Superior Court Judge William MacLaughlin ruled Monday.