Life for all animals starts with the fertilization of the egg, followed by the centration of the sperm nucleus and a 3D-choreography of reductive cell divisions called cleavage patterns. These invariant morphogenetic processes rely on the precise motion, positioning and orientation of large microtubule (MT) asters. Using a combination of mathematical models and quantitative experiments in sea urchin and other systems, we demonstrate that the geometry of eggs and blastomeres may influence these early morphogenetic events. Our data support that dynein-dependent MT cytoplasmic pulling forces that scale to MT length may function as a general design to convert cell shape into aster motion, position and orientation. This design allows to account for the centration of sperm nuclei at fertilization, as well as the geometry of cleavage patterns in multiple invertebrate and vertebrate species. These studies unravel the default self-organization rules governing early embryogenesis.