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We elucidate the dispersion behavior of deep-subwavelength propagating modes in coaxial plasmonic structures by making an explicit connection with the planar metal-insulator-metal geometry. We provide an intuitive picture that allows for a qualitative understanding and a quantitative prediction of the entire dispersion behavior, which includes the number of modes at every frequency, the modal propagation constants, the propagation losses, and the cutoff frequencies of propagating modes supported by these technologically important structures. We validate our analytical approach by comparing its predictions to first-principles finite-difference frequency-domain simulations.