The authors show which is the nanostructure required in granular Co20(ZrO2)80 thin films to produce an ac response such as the one that is universally observed in a very wide variety of dielectric materials. A bimodal size distribution of Co particles yields randomly competing conductance channels which allow both the thermally assisted tunneling through small particles and capacitive conductance among larger particles that are further apart. A model consisting on a simple cubic random resistance-capacitor network describes quantitatively the experimental results as functions of temperature and frequency, and enables the determination of the microscopic parameters controlling the ac response of the samples.