Knowledge of the human nanoscale connectome is crucial for understanding brain function in health and disease. However, the data required to construct a complete nanoscale connectome remain unavailable, and the exact numbers of circuits forming the connectome and neurons within each circuit are still unknown. This study introduces nanoscale morphologic connectomic wireframe and geometric models, each comprising three sub-models (straight and enhanced with parabolic and cubic branches); provides formulas to estimate their data bigness; and assesses required storage. The connectome size/storage estimation builds upon prior work on the synaptome (complete synapse set). To account for the great variability in neuronal and synaptic counts, two estimates for the total number of brain neurons (86 and 100 billion) and three estimates for synapses-per-neuron (1,000;10,000; and 30,000) are considered across six connectomic models, yielding 36 storage estimation cases. The straight wireframe model requires from 8.51 PB (for 86 billion neurons, 1,000 synapses-per-neuron) to 297 PB (for 100 billion neurons, 30,000 synapses-per-neuron). The straight geometric model needs from 10.58 PB (for 86 billion neurons, 1,000 synapses-per-neuron) to 369 PB (for 100 billion neurons, 30,000 synapses-per-neuron). Model enhancement significantly increases storage from 22.27 PB for the parabolic wireframe model (for 86 billion neurons, 1,000 synapses-per-neuron) to 1,569 PB for the cubic geometric model (for 100 billion neurons, 30,000 synapses-per-neuron). The storage required for the complete human nanoscale connectome, as estimated for six models and 36 cases, exceeds the capacity of today’s most powerful supercomputers. This work is the first providing the bigness data estimation for representing the entire human nanoscale connectome.