  Motivated by recent observational studies of the environment of z~6 QSOs, we
have used the Millennium Run (MR) simulations to construct a very large (~20
deg^2) mock redshift survey of star-forming galaxies at z~6. We use this
simulated survey to study the relation between density enhancements in the
distribution of i-dropouts and Lya-emitters, and their relation to the most
massive halos and protocluster regions at z~6. Our simulation predicts
significant variations in surface density across the sky with some voids and
filaments extending over scales of 1 degree, much larger than probed by current
surveys. Approximately one third of all z~6 halos hosting i-dropouts brighter
than z=26.5 mag (~M* at z=6) become part of z=0 galaxy clusters. i-dropouts
associated with protocluster regions are found in regions where the surface
density is enhanced on scales ranging from a few to several tens of arcminutes
on the sky. We analyze two structures of i-dropouts and Lya-emitters observed
with the Subaru Telescope and show that these structures must be the seeds of
massive clusters-in-formation. In striking contrast, six z~6 QSO fields
observed with HST show no significant enhancements in their i-dropout number
counts. With the present data, we cannot rule out the QSOs being hosted by the
most massive halos. However, neither can we confirm this widely used
assumption. We conclude by giving detailed recommendations for the
interpretation and planning of observations by current and future ground- and
space based instruments that will shed new light on questions related to the
large-scale structure at z~6.
