The large theropod dinosaur Tyrannosaurus rex underwent remarkable changes during its growth from <10 kg hatchlings to >6000 kg adults in <20 years. These changes raise fascinating questions about the morphological transformations involved, peak growth rates, and scaling of limb muscle sizes as well as the body's centre of mass that could have influenced ontogenetic changes of locomotion in T. rex. Here we address these questions using three-dimensionally scanned computer models of four large, well-preserved fossil specimens as well as a putative juvenile individual. Furthermore we quantify the variations of estimated body mass, centre of mass and segment dimensions, to characterize inaccuracies in our reconstructions. These inaccuracies include not only subjectivity but also incomplete preservation and inconsistent articulations of museum skeletons. Although those problems cause ambiguity, we conclude that adult T. rex had body masses around 6000-8000 kg, with the largest known specimen ("Sue") perhaps ~9500 kg. Our results show that during T. rex ontogeny, the torso became longer and heavier whereas the limbs became proportionately shorter and lighter. Our estimates of peak growth rates are about twice as rapid as previous ones but generally support previous methods, despite biases caused by the usage of scale models and equations that underestimate body masses. We tentatively infer that the hindlimb extensor muscles masses, including the large tail muscle M. caudofemoralis longus, may have decreased in their relative size as the centre of mass shifted craniodorsally during T. rex ontogeny. Such ontogenetic changes would have worsened any relative or absolute decline of maximal locomotor performance. Regardless, T. rex probably had hip and thigh muscles relatively larger than any extant animal's. Overall, the limb "antigravity" muscles may have been as large as or even larger than those of ratite birds, which themselves have the most muscular limbs of any living animal.