The cleavage furrow in zygotes is positioned by two large microtubule asters that grow out from the poles of the first mitotic spindle. Where these asters meet at the midplane, they assemble a disk-shaped interaction zone consisting of anti-parallel microtubule bundles coated with chromosome passenger complex (CPC) and centralspindlin that instructs the cleavage furrow. Here we investigate the mechanism that keeps the two asters separate and forms a distinct boundary between them, focusing on the conserved cytokinesis midzone proteins Prc1 and Kif4A. Prc1E, the egg orthologue of Prc1, and Kif4A were recruited to anti-parallel bundles at interaction zones between asters in egg extracts. Prc1E was required for Kif4A recruitment but not vice versa. Microtubule plus-end growth slowed and terminated preferentially within interaction zones, resulting in a block to interpenetration that depended on both Prc1E and Kif4A. Unexpectedly, Prc1E and Kif4A were also required for radial order of large asters growing in isolation, apparently to compensate for the direction-randomizing influence of nucleation away from centrosomes. We propose that Prc1E and Kif4, together with catastrophe factors, promote "anti-parallel pruning" that enforces radial organization within asters and generates boundaries to microtubule growth between asters.