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 \lesssim 4 ) are observed on the disc half-thickness .
The sensitivity of the results to the \alpha -parameter value has been tested for 0.001 \leq \alpha \leq 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 .