Using a molecular dynamics and mean field theory approach which explicitly accounts for free ions, we study the conformation of polyelectrolyte dendrimers for different generation numbers, spacer lengths, charge distributions and ionic strengths. We find that, due to local charge neutrality, electrostatic interactions are strongly screened under all the conditions studied (including salt free conditions). This leads to the cores of the dendrimers being filled and to a very weak dependence of dendrimer conformations on ionic strength. These results are contrary the predictions of Debye-Huckel theory and highlight the limitations of Debye-Huckel theory in modeling the properties of highly charged macromolecular systems. However, our simulations suggest that some responsiveness to ionic strength may be recovered for more weakly charged dendrimers.