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Liquid-liquid phase separation has received growing interest due to the newly recognized role it plays in biological systems in the formation of condensates. Some biological fluids can, under certain conditions, exhibit liquid crystallinity. It is unknown how this liquid crystallinity may impact condensate formation and the shape of condensate domains. This work examines phase separation in synthetic systems that are a mixture of a liquid crystal mesogen and a simple solvent. While interfacial forces generally drive the formation of discrete spherical condensates that coalesce into macroscopic domains, our work has shown that liquid-liquid crystal systems can form sample-spanning filamentous networks. The formation of these networks is difficult to study due to highly dynamic interaction of many growing filaments. By confining this phase separation to microdroplets, we are better able to observe filament dynamics and we find that filament morphology is determined by an interplay of interfacial forces, distortion of the smectic layers, and geometric confinement. We observe a characteristic relationship between drop and filament radius. This relationship appears to be mediated by the evolution of filaments by intermittent collapse, where some critical threshold length is reached, and the filament coalesces before regrowing with a thicker fixed radius. High-speed imaging suggests that the collapse mechanism itself may be mediated by filament-filament contact which propagates by zipping and twisting. Further exploration of this system may yield insights into biological condensates, smectic behavior under non-equilibrium dynamics, or new materials.