The ac conductance in granular insulating Co-ZrO 2 thin films prepared by pulsed laser deposition is systematically studied as a function of the Co volume content x . An absorption phenomenon at low frequencies that mimics the universal response of disordered dielectric materials is observed in the range of metal content below the Co percolation threshold x p ≈ 0.35 in the so-called dielectric regime. The temperature and frequency dependences of this absorption phenomenon are successfully analyzed in terms of random competing conduction channels between Co particles through thermally assisted tunneling and capacitive conductance. The ac conductance is well correlated with the nanostructure of the samples obtained by the transmission electron microscopy and perfectly matches the calculated ac response for a random resistor-capacitor network. We also show the occurrence of fractional power-law dependences on the frequency of the ac conductance taking place at very low frequencies as compared to the typical ranges at which dispersive behavior is observed in classical-disordered dielectric materials.