  We present new measurements of the spatial distribution and kinematics of
neutral hydrogen in the circumgalactic and intergalactic medium surrounding
star-forming galaxies at z ~ 2. Using the spectra of ~ 3000 galaxies with
redshifts <z> +/- 0.4 from the Keck Baryonic Structure Survey (KBSS), we
assemble a sample of more than 200,000 distinct foreground-background pairs
with projected angular separations of 3 - 500 arcsec and spectroscopic
redshifts, with <$z_{fg}$> = 2.23 and <$z_{bg}$> = 2.57. The ensemble of
sightlines and foreground galaxies is used to construct a 2D map of the mean
excess Ly$\alpha$ optical depth relative to the intergalactic mean as a
function of projected galactocentric distance (20 < $D_{tran}$/pkpc < 4000) and
line-of-sight velocity. We provide information on the line-of-sight kinematics
of H I gas as a function of projected distance $D_{tran}$. We compare the map
with cosmological zoom-in simulation, finding qualitative agreement between
them. A simple two-component (accretion, outflow) analytical model generally
reproduces the observed line-of-sight kinematics and projected spatial
distribution of H I. The best-fitting model suggests that galaxy-scale outflows
with initial velocity $v_{out}$ ~ 600 km/s dominate the kinematics of
circumgalactic H I out to $D_{tran}$ ~ 50 kpc, while H I at $D_{tran}$ > 100
kpc is dominated by infall with characteristic $v_{in}$ < $v_c$, where $v_c$ is
the circular velocity of the host halo ($M_h$ ~ $10^{12} M_\odot$). Over the
impact parameter range 80 < $D_{tran}$/pkpc < 200, the H I line-of-sight
velocity range reaches a minimum, with a corresponding flattening in the
rest-frame Ly$\alpha$ equivalent width. These observations can be naturally
explained as the transition between outflow-dominated and accretion-dominated
flows. Beyond $D_{tran}$ ~ 300 kpc, the line of sight kinematics are dominated
by Hubble expansion.
