  We use high-resolution zoom-in simulations to study the fueling of the
central galaxies by gas accretion from cosmological filaments at high
redshifts, z>=2. Their parent haloes with similar DM masses of
log(M_vir/M})~11.65, have been chosen at z=6, 4, and 2, in high/low overdensity
environments, with the goal of comparing evolution within similar M at
different z, under dual action of cosmological accretion and galactic outflows
-- forming the circumgalactic medium (CGM). We focus on the filamentary and
diffuse gas accretion within few virial radii, R_vir, down to the central
galaxy. Using a hybrid d-web/entropy method we have mapped the gaseous
filaments, and invoking particle kinematics allowed us to separate inflows from
outflows, thus resolving thermodynamic and kinematic signatures of the CGM. We
find that (1) The CGM is multiphase and not in thermodynamic or dynamic
equilibrium; (2) accretion rates via individual filaments display a lower
accretion rate and densities at lower redshifts. The inflow velocities along
the filaments decrease with redshift, z~ 6-2, from 200-30 kms^-1 by a factor of
2; (3) Temperature within the filaments increases inside R_vir, faster at lower
redshifts, in tandem with decrease in the accretion rate; (4) The filaments
show a complex structure along their spines: a core radial flow surrounded by a
lower density envelope. The core exhibits an elevated density and lower
temperature, with no obvious metallicity gradient in the filament cross
sections. It also tends to separate the filament into different infall velocity
regions and density cores, thus producing a spaghetti-type flow; (6) Inside the
inner ~ 30\,h^-1 kpc, the filaments develop the Kelvin-Helmholtz instability
which ablates and dissolves them, and triggers turbulence along the filament
spine; (7) Finally, the galactic outflows affect mostly the inner ~ 0.5R_vir~
100 h^-1 kpc of the CGM.
