We propose a simple method for calculating the ground state wavefunction of an electron–hole pair confined in a heterostructure formed by a flat quantum dot deposited on a thin wetting layer and imbedded in a matrix made of other material. The calculations of the exciton ground state energy, the electron–hole space pair correlation function and the density of the charge distribution have been performed for In0.55Al0.45As–Al0.35Ga0.65As and Ga0.7Al0.3As/GaAs quantum discs and rings. It is shown that the increase of the wetting layer thickness and the strength of the external magnetic field applied parallel to the axis lead to a lowering of the inner barrier height reinforcing the tunnelling of the particles into the central hole region. We also analyse the charge distribution related to the spatial separation of the particles due to the difference between masses of the electron and the hole. The variation of the quadrupole momentum sign with the increase of the ring inner radius and the appearance of the dipole momentum oriented in the crystal growth direction with the increase of the wetting layer thickness in the presence of the electron–hole pair are predicted.