By comparison to a gold standard multiparametric mapping (MPM) protocol at 3T, this study shows that multi-echo 3D-EPI with highly segmented CAIPIRINHA sampling can yield whole-head T1, PD*, MTsat and R2* maps of high quality at 1mm isotropic resolution in less than 3 minutes scan time. Even less than 1 minute of single-echo 3D-EPI is sufficient to yield accurate quantitative T1, PD* and MTsat maps. If necessary, SNR can be improved by including repeated EPI measurements. Optional motion- and distortion-correction across measurements may further improve results. Motion-robust MPM thus renders assessing quantitative parameter maps in clinical or population studies feasible.