We report on the optical spectroscopy of a series of ZnO/(Zn, Mg)O quantum wells of different widths, using time-resolved photoluminescence. The samples were grown by molecular beam epitaxy on ZnO templates, themselves deposited on sapphire substrates. The barriers consist of Zn0.78Mg0.22O layers. The presence of large internal electric fields in these quantum wells results in a competition between quantum confinement and the quantum confined Stark effect as the quantum well width is varied. A transition energy lying 0.5 eV below the ZnO excitonic gap was observed for the widest of our wells. The PL spectra of the wide quantum wells were obtained using time-integrated photoluminescence, taking a great care with screening effects induced by their very slow dynamics. The effect of the built-in electric field on the excitonic properties was investigated. The excitonic fine structure is shown to depend strongly on the enhancement or suppression of the exchange interaction as a function of the quantum well width.