  We probe the geometry of magnetospheric accretion in classical T Tauri stars
by modeling red absorption at He I 10830 via scattering of the stellar and
veiling continua. Under the assumptions that the accretion flow is an
azimuthally symmetric dipole and helium is sufficiently optically thick that
all incident 1-micron radiation is scattered, we illustrate the sensitivity of
He I 10830 red absorption to both the size of the magnetosphere and the filling
factor of the hot accretion shock. We compare model profiles to those observed
in 21 CTTS with subcontinuum redshifted absorption at He I 10830 and find that
about half of the stars have red absorptions and 1-micron veilings that are
consistent with dipole flows of moderate width with accretion shock filling
factors matching the size of the magnetospheric footpoints. However, the
remaining 50% of the profiles, with a combination of broad, deep absorption and
low 1-micron veiling, require very wide flows where magnetic footpoints are
distributed over 10-20% of the stellar surface but accretion shock filling
factors are < 1%. We model these profiles by invoking large magnetospheres
dilutely filled with accreting gas, leaving the disk over a range of radii in
many narrow "streamlets" that fill only a small fraction of the entire infall
region. In some cases accreting streamlets need to originate in the disk
between several stellar radii and at least the corotation radius. A few stars
have such deep absorption at velocities greater than half the stellar escape
velocity that flows near the star with less curvature than a dipole trajectory
seem to be required.
