We use high-resolution zoom-in simulations to study the fueling of central galaxies by filamentary and diffuse accretion at redshifts, z ≳ 2. The parent haloes were chosen with similar total masses, log (Mvir/M⊙) ∼ 11.75 ± 0.05, at z = 6, 4, and 2, in high/low overdensity environments. We analyze the kinematic and thermodynamic properties of circumgalactic medium (CGM) within few virial radii, Rvir, and down to the central galaxy. Using a hybrid d-web/entropy method we mapped the gaseous filaments, and separated inflows from outflows. We find that (1) The CGM is multiphase and not in thermodynamic or dynamic equilibrium; (2) filamentary and diffuse accretion rates and densities decrease with lower redshifts, and inflow velocities decrease from 200 − 300 km s−1 by a factor of 2; (3) temperature within the filaments increases inside Rvir, faster at lower redshifts; (4) filaments show a complex structure along their spines: a core radial flow surrounded by a lower density envelope. The cores exhibit elevated densities and lower temperature, with no obvious metallicity gradient in the cross sections. Filaments also tend to separate into different infall velocity regions and split density cores, thus producing a spaghetti-type flow; (6) inside the inner ∼30 h−1 kpc, filaments develop the Kelvin-Helmholtz instability which ablates and dissolves them, and triggers turbulence along the filaments, clearly delineating their spines; (7) finally, the galactic outflows affect mostly the inner ∼0.5Rvir ∼ 100h−1kpc of the CGM.