Six men paid about $55 million for the company in 2012. Katz and Lenfest own about 42 percent of IGM; Norcross bought out one partner and now owns about 52 percent.
When, where, and in what form their bidding war takes place is likely to be decided by a judge.
In court filings last week, Katz and Lenfest asked for a public auction. Norcross wants a private bidding contest confined to the current owners.
Common Pleas Court Judge Patricia A. McInerney, who granted Katz's request last fall for an injunction reinstating fired Inquirer editor William K. Marimow, was assigned Tuesday to oversee Katz's petition to dissolve the embattled partnership and move to a public sale.
No hearings have been scheduled.
Lawyers for Norcross have up to 20 days to file a response. They have also filed a parallel request in Delaware, where the company was incorporated. That petition is pending in Chancery Court. No judge has been assigned there.
Lawyers who have handled corporate dissolutions and who asked not to be named say the process can take six to eight months.
According to their filings, both sides agree that the dispute could paralyze or has paralyzed the company, which employs about 1,800 workers at The Inquirer, the Philadelphia Daily News, and Philly.com.
Under an agreement, all major IGM decisions must be approved by Norcross and Katz. But the owners and managing partners are "mired in litigation and are deadlocked under a governing document that provides no means of resolving the deadlock," Katz and Lenfest's petition says.
Norcross' petition notes major decisions that are looming: the potential need to find a new editor for The Inquirer after Marimow's contract expires April 30, and the need to recruit a replacement for publisher Robert J. Hall, who wants to retire.
In their filing, Katz and Lenfest's lawyers propose an open auction, with each bidder submitting one sealed bid for all of the company's assets.
The Delaware petition did not lay out how a private sale might proceed, but in a letter Friday to Katz, Norcross and co-owner William P. Hankowsky reiterated a proposal for a "blitz" auction, with the five owners each making a $4 million security deposit and bidding against each other in $1 million increments.
A private auction would cost less to run and would protect the company from outside investors who might slash jobs, Norcross and Hankowsky said in a letter to employees.
Newspaper Guild president Howard Gensler said the union, which represents many newsroom and other employees and whose leadership met Tuesday, was not taking sides.
"There are pros and cons to a private auction and to a public auction," Gensler said. "We're trying to figure out which approach offers our members the best chance for a stable, profitable future."
Inquirer staff writer David Sell contributed to this article.