brokenmandible sends in word that TNT is planning to run all three LOTR films on Starz in High Definition. The bad part is that they are encoding them in Segments, which means that they will have commercial interruption. They also are only 3 hours in duration approximately, therefore they are NOT the extended editions.
UPDATE: These definitely are NOT for CINEMAX, These have the TNT logo branded on them. They will be on TNT since they now have an HD channel.