The study of brain structural asymmetries as anatomical substrates of functional asymmetries in extant humans, great apes, and fossil hominins is of major importance in understanding the structural basis of modern human cognition. We propose methods to quantify the variation in size, shape and bilateral asymmetries of the third frontal convolution (or posterior inferior frontal gyrus) among recent modern humans, bonobos and chimpanzees, and fossil hominins using actual and virtual endocasts. These methodological improvements are necessary to extend previous qualitative studies of these features. We demonstrate both an absolute and relative bilateral increase in the size of the third frontal convolution in width and length between Pan species, as well as in hominins. We also observed a global bilateral increase in the size of the third frontal convolution across all species during hominin evolution, but also non-allometric intra-group variations independent of brain size within the fossil samples. Finally, our results show that the commonly accepted leftward asymmetry of Broca's cap is biased by qualitative observation of individual specimens. The trend during hominin evolution seems to be a reduction in size on the left compared with the right side, and also a clearer definition of the area. The third frontal convolution considered as a whole projects more laterally and antero-posteriorly in the right hemisphere. As a result, the left 'Broca's cap' looks more globular and better defined. Our results also suggest that the pattern of brain asymmetries is similar between Pan paniscus and hominins, leaving the gradient of the degree of asymmetry as the only relevant structural parameter. As the anatomical substrate related to brain asymmetry has been present since the appearance of the hominin lineage, it is not possible to prove a direct relationship between the extent of variations in the size, shape, and asymmetries of the third frontal convolution and the origin of language in hominins.