Normative modeling is a statistical approach to quantify the degree to which a particular individual-level measure deviates from the pattern observed in a normative reference population. When applied to human brain morphometric measures it has the potential to inform about the significance of normative deviations for health and disease. Normative models can be implemented using a variety of algorithms that have not been systematically appraised. To address this gap, eight algorithms were compared in terms of performance and computational efficiency using brain regional morphometric data from 37,407 healthy individuals (53.33% female; aged 3 to 90 years) collated from 86 international MRI datasets. Performance was assessed with the mean absolute error (MAE) and computational efficiency was inferred from central processing unit (CPU) time. The algorithms evaluated were Ordinary Least Squares Regression (OLSR), Bayesian Linear Regression (BLR), Generalized Additive Models for Location, Scale, and Shape (GAMLSS), Parametric Lambda, Mu, Sigma (LMS), Multivariable Fractional Polynomial Regression (MFPR), Warped Bayesian Linear Regression (WBLG), and Hierarchical Bayesian Regression (HBR). Model optimization involved testing 9 covariate combinations pertaining to acquisition features, parcellation software versions, and global neuroimaging measures (i.e., total intracranial volume, mean cortical thickness, and mean cortical surface area). Statistical comparisons across models at PFDR<0.05 indicated that MFPR-derived sex and region-specific models with nonlinear polynomials for age and linear effect of global measures had superior predictive accuracy; for models of regional subcortical volume the MAE range was 70-80 mm3 and the corresponding range for regional cortical thickness and regional cortical surface area was 0.09-0.26 mm; and 24-660 mm2 respectively. The MFPR-derived models were also computationally more efficient with a CPU time below one second compared to a range of 2 seconds to 60 minutes for the other algorithms. MFPR-derived models were robust across distinct age groups when sample sizes exceeded 3,000. These results support CentileBrain (https://centilebrain.org/) an empirically benchmarked framework for normative modeling that is freely available to the scientific community.