Asymmetric cell division, where daughter cells inherit unequal amounts of specific factors, is critical for development and cell fate specification. In polarized cells, where specific factors are segregated to opposite ends of the cell, asymmetric cell division occurs as a result of positioning the centrosomes along the polarity axis. Using an individual-based stochastic model of centrosome-associated microtubule dynamics and experiments in early embryos of the nematode worm C. elegans, we explore potential sources of force generation and demonstrate the role of both cortical and centrosomal asymmetries for recapitulating the in vivo dynamics and proper positioning of the centrosomes prior to first division.