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Mechanisms underlying the organization of centrosomal microtubule arrays are well understood, but less is known about how acentrosomal microtubule networks are formed. The basal cortex of polarized epithelial cells contains a microtubule network. We examined how this network is organized by imaging microtubule dynamics in cytoplasts derived from these cells. We show that the steady-state microtubule network appears to form by a combination of microtubule-microtubule and microtubule-cortex interactions, both of which increase microtubule stability. We used computational modeling to determine whether these microtubule parameters are sufficient to generate a steady-state microtubule network. Microtubules undergoing dynamic instability without any stabilization points continuously remodel their organization without reaching a steady-state network. However, the addition of increased microtubule stabilization at microtubule-microtubule and microtubule-cortex interactions results in the rapid assembly of a steady-state microtubule network in silico that is remarkably similar to networks formed in situ. These results define minimal parameters for the self-organization of an acentrosomal microtubule network.