Structural asymmetries of brain regions associated with lateralised functions have been extensively studied. However, there are fewer morphometric analyses of asymmetries of the gyri and sulci of the entire cortex. The current study assessed cortical asymmetries in a sample of healthy adults (N = 175) from an admixed population from South America. Grey matter volume and surface area of 66 gyri and sulci were quantified on T1 magnetic resonance images. The departure from zero of the differences between left and right hemispheres (L-R), a measure of directional asymmetry (DA), the variance of L-R, and an index of fluctuating asymmetry (FA) were evaluated for each region. Significant departures from perfect symmetry were found for most cortical gyri and sulci. Regions showed leftward asymmetry at the population level in the frontal lobe and superior lateral parts of the parietal lobe. Rightward asymmetry was found in the inferior parietal, occipital, frontopolar, and orbital regions, and the cingulate (anterior, middle, and posterior-ventral). Despite this general pattern, several sulci showed the opposite DA compared to the neighbouring gyri, which remarks the need to consider the neurobiological differences in gyral and sulcal development in the study of structural asymmetries. The results also confirm the absence of DA in most parts of the inferior frontal gyrus and the precentral region. This study contributes with data on populations underrepresented in the databases used in neurosciences. Among its findings, there is agreement with previous results obtained in populations of different ancestry and some discrepancies in the middle frontal and medial parietal regions. A significant DA not reported previously was found for the volume of long and short insular gyri and the central sulcus of the insula, frontomarginal, transverse frontopolar, paracentral, and middle and posterior parts of the cingulate gyrus and sulcus, gyrus rectus, occipital pole, and olfactory sulcus, as well as for the volume and area of the transverse collateral sulcus and suborbital sulcus. Also, several parcels displayed significant variability in the left-right differences, which can be partially attributable to developmental instability, a source of FA. Moreover, a few gyri and sulci displayed ideal FA with non-significant departures from perfect symmetry, such as subcentral and posterior cingulate gyri and sulci, inferior frontal and fusiform gyri, and the calcarine, transverse collateral, precentral, and orbital sulci. Overall, these results show that asymmetries are ubiquitous in the cerebral cortex.