Laelaps

Dawn glows along the shore of a lagoon near the sea three millions of years ago in Montana. The landscape is of low relief; sycamores and ginkgo trees mingle with figs, palms and bananas. There are few twittering birds in the tree-tops and no herds of grazing animals to greet the early sun. A huge herbivorous dinosaur Trachodon, coming on shore for some favorite food has been seized and partly eaten by a giant Tyrannosaurus. Whilst this monster is ravenously consuming the carcass another Tyrannosaurus draws near determined to dispute the prey. The stooping animal hesitates, partly rises and prepares to spring on its opponent. With colossal bodies poised on massive hind legs and steadied by long tails, ponderous heads armed with sharp dagger-like teeth three to five inches long, front limbs exceedingly small but set for a powerful clutch, they are the very embodiment of dynamic animal force. - Barnum Brown, "Tyrannosaurus, the Largest Flesh-Eating Animal That Ever Lived." 1915

Such was the battle that Brown and his employer, H.F. Osborn, wanted to reconstruct at the American Museum of Natural History, but it never came to be. The first Tyrannosaurus skeleton that Brown uncovered was sold to the Carnegie museum, and the second (far-more complete) specimen stayed in New York. Still, even in 1915 there was still hope of bringing the elaborate scene to life. By 1915 the second skeleton ("the challenger") was already mounted, and as Brown says in at the conclusion of the article;

The sudden pause in its forward rush on coming close to its crouching enemy is well suggested, but the attitude could be more clearly seen if the outlines of the flesh of the body and limbs were restored.

As already stated, however, the second Tyrannosaurus was sold, and the larger project abandoned. Brown's baby stood alone, threatening a rival that wasn't there, until the mount was taken down and revised in the 1990's. Interestingly, though, Osborn & Brown's concept got a second lease at life when the Carnegie Museum (to which the 1st Tyrannosaurus was sold) recently revamped their dinosaur exhibit. Although I have not seen it explicitly stated, the folks at the Carnegie picked up the idea of rival rexes and reconstructed the scene based upon what we know about Tyrannosaurus now. I have not been able to visit the museum to see it myself, but I bet that Brown would have been impressed.