Paramount chief Brad Grey, who produces “The Sopranos” and has represented countless Hollywood heavyweights, is now in the center of a legal tug of war that could wind up with him invoking his Fifth Amendment rights in nasty depositions.

Thanks to a 5-year-old lawsuit between Grey and movie producer Vincent Bo Zenga over the satire, “Scary Movie,” Grey has managed to edge out both attorney Bert Fields and former agent Michael Ovitz as the three jockey for position in who can get their names out of the Pellicano story with the least damage.

Yesterday in Los Angeles Superior Court, Zenga’s attorney Gregory Dovel filed a strong answer to a motion made by Grey’s attorney’s a couple of weeks ago.

This all stems from articles that appeared here on March 17 and 24: The government’s massive indictment against Anthony Pellicano included the information that during depositions for that “Scary Movie” lawsuit, Pellicano illegally wiretapped and investigated Zenga, members of his family and Dovel.

Zenga went on to lose the actual case. But since the revelations in the February 2006 indictment, he has asked the court to throw out the verdict, bring in the information from the indictment and start again.

Grey, of course, is opposing this. His lawyers essentially argued in their answer a couple of weeks ago that the Pellicano indictment has nothing to do with the fact that Grey won the original case against Zenga over who really produced “Scary Movie” and was entitled to credit and money from it.

Grey’s motion to “stay,” or halt, the discovery of materials in Zenga’s new suit is interesting because of his claim — that prosecutors in the Pellicano case, while still gathering evidence for their case, have handed some of the evidence to Zenga.

The argument is that the government is using Zenga’s case to test their evidence, and that it shouldn’t be allowed.

In his answer, Dovel essentially says that Zenga’s new lawsuit should be able to go forward no matter what’s happening in the U.S. vs. Pellicano.

Dovel writes that in this litigation, Zenga seeks to protect his constitutionally protected right not be subject to an invasion of privacy, and to redress a wrong that strikes at the core of our judicial system.

The judge, who will hear all this in open court on June 1, will have to decide if it matters that Grey is now only considered a “witness” in the Pellicano case and not a more important participant.

Dovel will argue that it’s because Grey is indeed only a witness that Zenga’s case should go forward.

It sounds like a boring legal exercise, but if Grey loses this argument, he could wind up testifying in depositions about his involvement in Pellicano’s wiretapping — and invoking his Fifth Amendment privileges.

Grey’s answer to the Fifth Amendment question is that in their original “Scary Movie” suit, Zenga used the Fifth Amendment many times in order not to answer questions.

That much is true; it’s on the record from the case.

But Dovel’s response is essentially, “Don’t confuse me with the facts.” In other words: This is now about Zenga being spied on by Grey, not about what Zenga has done in the past.

Because of this past situation with Zenga, Grey — at least in the court of public opinion — is fast becoming topic No. 1 among Hollywood insiders in the Pellicano saga.

That’s pretty amazing, considering that Pellicano has now had several prominent official fellow indictees in his case, including attorney Terry Christensen. “Die Hard” movie director John McTiernan has already pled guilty to using Pellicano for nefarious purposes.

But Grey, because he’s been elevated to a studio chief’s job since this started, is more interesting.

Fields is considered by wags too old at 78 to go to jail. Ovitz, while young enough, has moved to the side in Hollywood and isn’t an active player. Grey, however, has had a target painted on his side simply by virtue of being the most vulnerable of the trio.

Lately, gossip has swirled that he’s about to step aside or be removed from his post. His possible successors — Jeffrey Katzenberg, Stacey Snider, Lorenzo di Bonaventura — have made for a parlor game.

The latest theory abounding between Melrose and Monaco is that Viacom chief Tom Freston is headed to the West coast soon to take the reigns from Grey and regain some kind of authority.

But Grey’s supporters point out that he wouldn’t be coming to Cannes this weekend to launch so many projects (see above) if that were the case.