Using Monte Carlo simulations based on the bond fluctuation model, we study the behavior of a charged dendrimer grafted on one of the electrodes of a plate capacitor in an athermal, salt-free solvent. The calculations are performed for the full Coulomb potential in a wide range of parameters determining the strength of the electrostatic interactions between the charges and the magnitude of electric fields between the electrodes. For low temperatures and without an external field the dendrimer is in an osmotic regime where entropy of the trapped counterions controls the size of the molecule. Increasing the field strength leads to gradual removal of trapped counterions being localized at the opposite electrode. At a threshold value of the displacement field, D*, all counterions are stripped from the dendrimer, and the molecule is collapsed on the electrode. The collapse of the extension of the dendrimer in the direction perpendicular to the electrode is very sharp, and a bimodal distribution of monomers in the regime D < D* indicates a partial collapse of the dendrimer in this region. Here, uncompensated charges of the dendrimer are localized in substructures which are collapsed on the electrode while other parts of the molecule are still in the osmotic regime with respect to the remaining counterions. For higher temperature the collapse transition is smeared, and the osmotic effect of the counterions is less important.