How cortical neurons process information crucially depends on how their local circuits are organized. Spontaneous synchronous neuronal activity propagating through neocortical slices displays highly diverse, yet repeatable, activity patterns called "neuronal avalanches". They obey power-law distributions of the event sizes and lifetimes, presumably reflecting the structure of local circuits developed in slice cultures. However, the explicit network structure underlying the power-law statistics remains unclear. Here, we present a neuronal network model of pyramidal and inhibitory neurons that enables stable propagation of avalanche-like spiking activity. We demonstrate a neuronal wiring rule that governs the formation of mutually overlapping cell assemblies during the development of this network. The resultant network comprises a mixture of feedforward chains and recurrent circuits, in which neuronal avalanches are stable if the former structure is predominant. Interestingly, the recurrent synaptic connections formed by this wiring rule limit the number of cell assemblies embeddable in a neuron pool of given size. We investigate how the resultant power laws depend on the details of the cell-assembly formation as well as on the inhibitory feedback. Our model suggests that local cortical circuits may have a more complex topological design than has previously been thought.