We probe the geometry of magnetospheric accretion in classical T Tauri stars (CTTSs) by modeling red absorption at He I lambda10830 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 mum radiation is scattered, we illustrate the sensitivity of He I lambda10830 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 CTTSs with subcontinuum redshifted absorption at He I lambda10830 and find that about half of the stars have red absorption and 1 mum 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 mum veiling, require very wide flows where magnetic footpoints are distributed over 10%-20% of the stellar surface but accretion shock filling factors are 0.5Vesc that flows near the star with less curvature than a dipole trajectory seem to be required.