A judge who has presided over most of the litigation stemming from the Sept. 11, 2001, attacks will decide whether the owners of the World Trade Center can try to make aviation companies pay billions of dollars in damages.

U.S. District Judge Alvin K. Hellerstein said he will announce his decision immediately after hearing several witnesses and listening to arguments in a non-jury trial starting Monday and expected to last three days.

The trial will decide whether World Trade Center Properties and its affiliates can receive more than the $4.9 billion U.S. in insurance proceeds they have already recovered since the Sept. 11 attacks by extremists who hijacked commercial airliners and flew them into the 110-storey twin towers. The attacks led to the destruction of the towers as well as a third trade center building.

If the judge should decide that the WTC owners were entitled to additional money, a liability trial might occur. The defendants include American Airlines Inc., AMR Corp., United Airlines Inc., US Airways Inc., Colgan Air Inc., Boeing Co. and the Massachusetts Port Authority, among others.

The airlines and other aviation-related companies were sued with the reasoning that they were negligent, allowing terrorists to board airplanes and overtake their crews before plunging the planes into the trade center complex, destroying three buildings.

Hellerstein has already said the maximum the trade center owners could recover from aviation defendants would be $3.5 billion. The trade center owners say it has cost more than $7 billion to replace the twin towers and more than $1 billion to replace the third trade center building that fell.

In court papers, both sides have accused the other of unfairly characterizing their claims, with the aviation defendants saying the trade center owners were being "absurd" and the complex's owners labeling some of the aviation defendants' arguments as "nonsense."

The aviation defendants say Hellerstein should conclude that the trade center owners are entitled to no award because they've already been reimbursed by insurance companies for the same damage they are trying to force aviation defendants to pay for as well. They also note that the replacement buildings are more modern and fancy than the original buildings.

Of the 7 World Trade Center building — the first to be rebuilt after the attacks — the lawyers wrote that the trade center owners "built a new, state of the art 'green' building that bears little resemblance to the office building that collapsed as a result of the Sept. 11 terrorist attacks."

They said they plan to call only two witnesses: an expert on law and economics and an expert in the adjustment of insurance claims. Additional evidence they will introduce will include leases, insurance policies, proof of loss, communications between trade center leaseholders and their insurers, and financial statements.

In their court papers, the trade center's owners insist that recovering money from aviation defendants would not result in a "double recovery" because of the billions they've already received from insurers. And they note that their rebuilding costs "far exceed" what they've received from insurers.