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In light of the improved sensitivities of cosmological observations, we examine the status of quasi-degenerate neutrino mass scenarios. Within the simplest extension of the standard cosmological model with massive neutrinos, we find that quasi-degenerate neutrinos are severely constrained by present cosmological data and neutrino oscillation experiments. % % We find that Planck 2018 observations of cosmic microwave background (CMB) anisotropies disfavour quasi-degenerate neutrino masses at $2.4$ Gaussian $σ$'s, while adding Baryon acoustic oscillations (BAO) data brings the rejection to 5.9$σ$'s. % The highest statistical significance with which one would be able to rule out quasi-degeneracy would arise if the sum of neutrino masses is $Σm_ν= 60$ \meV (the minimum allowed by neutrino oscillation experiments); % indeed a sensitivity of 15 meV, as expected from a combination of future cosmological probes, would further improve the rejection level up to 17$σ$. % We discuss the robustness of these projections with respect to assumptions on the underlying cosmological model, and also compare them with bounds from $β$ decay endpoint and neutrinoless double beta decay studies.