There is a renewed surge in percolation-induced transport properties of
diverse nano-particle composites (cf. RSC Nanoscience & Nanotechnology Series,
Paul O'Brien Editor-in-Chief). We note in particular a broad interest in
nano-composites exhibiting sharp electrical property gains at and above
percolation threshold, which motivated us to revisit the classical setting of
percolation in random resistor networks but from a multiscale perspective. For
each realization of random resistor networks above threshold, we use network
graph representations and associated algorithms to identify and restrict to the
percolating component, thereby preconditioning the network both in size and
accuracy by filtering {\it a priori} zero current-carrying bonds. We then
simulate many realizations per bond density and analyze scaling behavior of the
complete current distribution supported on the percolating component. We first
confirm the celebrated power-law distribution of small currents at the
percolation threshold, and second we confirm results on scaling of the maximum
current in the network that is associated with the backbone of the percolating
cluster. These properties are then placed in context with global features of
the current distribution, and in particular the dominant role of the large
current tail that is most relevant for material science applications. We
identify a robust, exponential large current tail that: 1. persists above
threshold; 2. expands broadly over and dominates the current distribution at
the expense of the vanishing power law scaling in the small current tail; and
3. by taking second moments, reproduces the experimentally observed power law
scaling of bulk conductivity above threshold
