Diagnostic diagrams showing the EW of HeIIλ1640 versus various line ratios: HeII/Hγ, CIVλ1550/HeII, CIII]1909/HeII, and OIII]λ1665/HeII. The observational constraints on the HeII clump in the halo of GN-z11 are shown with golden symbols, while the observational constraints for the HeII emission obtained from the large aperture extraction are shown with green symbols. Circles are for EWs for which the continuum has been inferred from photometry, while squares show the EWs for which the continuum constraints have been inferred directly from the spectra. Purple stars show PopII models with different (absolute) metallicities (colour-coded with different purple shadings) and where the gas and stars are assumed to have the same metallicity. Blue circles are models of PopIII stars in a pristine gas; light blue squares are models of PopIII stars in a mildly enriched gas, specifically Z_gas = 10⁻⁵; light blue triangles are models of PopIII stars in a more enriched gas, specifically Z_gas = 10⁻⁴. The PopIII markers have different sizes depending on the stellar mass range assumed for the IMF, as indicated in the legend. Orange pentagons show the predictions for accreting DCBHs embedded in gas with different (absolute) metallicities.