Attempts to reproduce theoretically the width Γd⁎=80±10 MeV of the I(JP)=0(3+) d⁎(2380) dibaryon resonance established by the WASA-at-COSY Collaboration are discussed. The validity of associating the d⁎(2380) in quark-based models exclusively with a tightly bound ΔΔ configuration is questioned. The d⁎(2380) width and decay branching ratios into NNππ, NNπ and NN final states are studied within the Gal–Garcilazo hadronic model in which the d⁎(2380) is a πNΔ resonance embedded in the NNππ continuum some 80 MeV below the ΔΔ threshold. In particular, predictions are made for the branching ratios of the unobserved yet d⁎(2380)→NNπ decays which are suppressed in a purely-ΔΔ dibaryon model. A possible connection of the ABC effect observed in the pn→d⁎→dπ0π0 resonance reaction to the d⁎(2380) dibaryon is noted.