We report on a large-scale study of the distribution of globular clusters (GCs) throughout the Virgo cluster, based on photometry from the Next Generation Virgo Cluster Survey, a large imaging survey covering Virgos primary subclusters to their virial radii. Using the g, (g-i) color-magnitude diagram of unresolved and marginally-resolved sources, we constructed 2-D maps of the GC distribution. We present the clearest evidence to date showing the difference in concentration between red and blue GCs over the extent of the cluster, where the red (metal-rich) GCs are largely located around the massive early-type galaxies, whilst the blue (metal-poor) GCs have a more extended spatial distribution, with significant populations present beyond 83 (215 kpc) along the major axes of M49 and M87. The GC distribution around M87 and M49 shows remarkable agreement with the shape, ellipticity and boxiness of the diffuse light surrounding both galaxies. We find evidence for spatial enhancements of GCs surrounding M87 that may be indicative of recent interactions or an ongoing merger history. We compare the GC map to the locations of Virgo galaxies and the intracluster X-ray gas, and find good agreement between these baryonic structures. The Virgo cluster contains a total population of 67300$pm$14400 GCs, of which 35% are located in M87 and M49 alone. We compute a cluster-wide specific frequency S_N,CL=$2.8pm0.7$, including Virgos diffuse light. The GC-to-baryonic mass fraction is e_b=$5.7pm1.1times10^{-4} $and the GC-to-total cluster mass formation efficiency is e_t=$2.9pm0.5times10^{-5}$, values slightly lower than, but consistent with, those derived for individual galactic halos. Our results show that the production of the complex structures in the unrelaxed Virgo cluster core (including the diffuse intracluster light) is an ongoing process.(abridged)
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