Cellular structures are established and maintained through a dynamic interplay between assembly and regulatory processes. Self-organization of molecular components provides a variety of possible spatial structures: the regulatory machinery chooses the most appropriate to express a given cellular function. Here we study the extent and the characteristics of self-organization using microtubules and molecular motors as a model system. These components are known to participate in the formation of many cellular structures, such as the dynamic asters found in mitotic and meiotic spindles. Purified motors and microtubules have previously been observed to form asters in vitro. We have reproduced this result with a simple system consisting solely of multi-headed constructs of the motor protein kinesin and stabilized microtubules. We show that dynamic asters can also be obtained from a homogeneous solution of tubulin and motors. By varying the relative concentrations of the components, we obtain a variety of self-organized structures. Further, by studying this process in a constrained geometry of micro-fabricated glass chambers, we demonstrate that the same final structure can be reached through different assembly 'pathways.