  Context: While classical models successfully reproduce intensities of many
transition region lines, they predict helium EUV line intensities roughly an
order of magnitude lower than the observed value.
  Aims: To determine the relevant formation mechanism(s) of the helium EUV
resonance lines, capable of explaining the high intensities under quiet sun
conditions.
  Methods: We synthesise and study the emergent spectra from a 3D
radiation-magnetohydrodynamics simulation model. The effects of coronal
illumination and non-equilibrium ionisation of hydrogen and helium are included
self-consistently in the numerical simulation.
  Results: Radiative transfer calculations result in helium EUV line
intensities that are an order of magnitude larger than the intensities
calculated under the classical assumptions. The enhanced intensity of He I 584
is primarily caused by He II recombination cascades. The enhanced intensity of
He II 304 and He II 256 is caused primarily by non-equilibrium helium
ionisation.
  Conclusion: The analysis shows that the long standing problem of the high
helium EUV line intensities disappears when taking into account optically thick
radiative transfer and non-equilibrium ionisation effects.
