The right-left lateralization of cognitive abilities in the human brain is reflected in hemispheric asymmetries. Since abnormal deviations of these asymmetries were linked to neurological disorders, establishing reference norms of hemispheric lateralization has clinical relevance. To this end, the normal evolution of brain asymmetries during development was modelled in a cohort of healthy young subjects. Normative ranges for brain asymmetries in volumes and T1 were established using a linear model while accounting for sex differences and age. Initial results in data of epileptic patients demonstrate the potential of the established norms for detecting abnormal brain lateralization on a single-subject basis.