Zero-lag and near zero-lag synchronization occur during certain stages of cognitive tasks. Accordingly, lag-free synchronization have been proposed to play a functional role as a binding process: to integrate the outcome of distributed and more specialized brain regions. Here we examine the synchronization of distant brain regions under the dynamical relaying framework. The main idea consists of introducing a third relay element bidirectionally delay-coupled with the two separated cortical regions. We numerically show that the dynamical relaying mechanism contributes to lag-free cortico-cortical synchronization in a broad range of oscillatory brain rhythms. The proposed model is very robust and relies on very general properties of oscillatory systems. We cogitate about the nature of the relay station, and incisively investigate the relay area as being another cortical region, the thalamus and the hippocampus. Remarkably, thalamic relay may control whether or not the zero-lag cortical synchronization is expected to emerge in beta or gamma bands. Moreover, for theta rhythms, the dynamical relaying typical signature is found in both simulations and \"in vivo\" mouse local field potential simultaneous recordings experiments. Altogether, based on phase synchronization, our results suggest that the dynamical relaying could be a widespread mechanisms involved in the integration of brain activity.
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