The phenomenal diversity of neuronal types in the central nervous system is achieved in part by the asymmetric division of neural precursors. In zebrafish neural precursors, asymmetric dispatch of Sara endosomes (with its Notch signaling cargo) functions as fate determinant which mediates asymmetric division. Here, we found two distinct pools of neural precursors based on Sara endosome inheritance and spindle-microtubule enrichment. Symmetric or asymmetric levels of spindle-microtubules drive differently Sara endosomes inheritance and predict neural precursor lineage. We uncover that CAMSAP2a/CAMSAP3a and KIF16Ba govern microtubule asymmetry and endosome motility, unveiling the heterogeneity of neural precursors. Using a plethora of physical and cell biological assays, we determined the physical parameters and molecular mechanisms behind microtubule asymmetries and biased endosome motility. Evolutionarily, the values of those parameters explain why all sensory organ precursor cells are asymmetric in flies while, in zebrafish spinal cord, two populations of neural precursors (symmetric vs asymmetric) are possible.