Cognitive processes depend on synchronization and propagation of electrical activity within and between neuronal assemblies. In vivo measurements show that the size of individual assemblies depends on their function and varies considerably, but the timescale of assembly activation is in the range of 0.1-0.2 s and is primarily independent of assembly size. Here we use an in vitro experimental model of cortical assemblies to characterize the process underlying the timescale of synchronization, its relationship to the effective topology of connectivity within an assembly, and its impact on propagation of activity within and between assemblies. We show that the basic mode of assembly activation, "network spike," is a threshold-governed, synchronized population event of 0.1-0.2 s duration and follows the logistics of neuronal recruitment in an effectively scale-free connected network. Accordingly, the sequence of neuronal activation within a network spike is nonrandom and hierarchical; a small subset of neurons is consistently recruited tens of milliseconds before others. Theory predicts that scale-free topology allows for synchronization time that does not increase markedly with network size; our experiments with networks of different densities support this prediction. The activity of early-to-fire neurons reliably forecasts an upcoming network spike and provides means for expedited propagation between assemblies. We demonstrate this capacity by observing the dynamics of two artificially coupled assemblies in vitro, using neuronal activity of one as a trigger for electrical stimulation of the other.