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We demonstrate high-electron-mobility transistors (HEMTs) based on InAlN/GaN nanoribbon (NR) structures. These devices, with NR widths d in the 50-90 nm range, are fabricated through a top-down technology on planar InAlN/GaN samples grown on a SiC substrate. The electrical properties of the InAlN/GaN NRs have been characterized by transmission-line model measurements and in HEMT structures, and compared with similar planar devices fabricated in close proximity. External mechanical stress and adequate surface passivation have a great impact on the NRs' performance. For example, when a thin Al2O3 dielectric is used to passivate the surface and to introduce tensile stress in the NR devices, the sheet resistance in the NRs becomes up to ~46% lower than that in passivated planar structures. These enhanced transport properties resulted in NR HEMTs with ~20-45% higher raw current than that in planar HEMTs. The NR technology combined with strain-passivation engineering allows the fabrication of NR HEMTs with record current densities (~2.9 A/mm) in the InAlN/GaN material system.