  We report the results of a systematic comparison between the vertically
averaged model and the vertically explicit model of steady state, Keplerian,
optically thick "alpha"-discs. The simulations have concerned discs currently
found in three different systems: dwarf novae, young stellar objects and active
galactic nuclei. In each case, we have explored four decades of accretion rates
and almost the whole disc area
  (except the narrow region where the vertically averaged model has degenerate
solutions). We find that the one layer approach gives a remarkably good
estimate of the main physical quantities in the disc, and specially the
temperature at the equatorial plane which is accurate to within 30% for cases
considered. The major deviations (by a factor < 4) are observed on the disc
half-thickness. The sensitivity of the results to the "alpha"-parameter value
has been tested for 0.001 < alpha < 0.1 and appears to be weak. This study
suggests that the ``precision'' of the vertically averaged model which is easy
to implement should be sufficient in practice for many astrophysical
applications.
