The intricacies of the core shell interaction in coaxial electrospinning are explored by way of the Hansen solubility parameters in an attempt to make micrometer-sized polymer-free multiwalled carbon nanotube (MWNT) core, poly(methyl methacrylate) shell fibers. Four solution regimes are explored in which the core solvent is either miscible or immiscible of the shell solvent and in which it is either a solvent or nonsolvent of the shell polymer. It is qualitatively found that the most well-defined MWNT bundle core is achieved using a core solvent that is semi-immiscible with the shell solution, yet still a solvent of the shell polymer. Hollow fibers are found to be produced best by using a core solvent that is immiscible with the shell solvent and also a nonsolvent of the shell polymer. The resulting MWNT-bundled cores are electrically characterized and found to have conductivities up to 2 orders of magnitude greater than homogeneously electrospun MWNT/polymer composite fibers.