  Previous analyses of magnetospheric accretion and outflow in classical T
Tauri stars (CTTSs), within the context of both the X-wind model and other
theoretical scenarios, have assumed a dipolar geometry for the stellar magnetic
field if it were not perturbed by the presence of an accreting, electrically
conducting disk. However, CTTS surveys reveal that accretion hot spots cover a
small fraction of the stellar surface, and that the net field polarization on
the stellar surface is small. Both facts imply that the magnetic field
generated by the star has a complex non-dipolar structure. To address this
discrepancy between theory and observations, we re-examine X-wind theory
without the dipole constraint. Using simple physical arguments based on the
concept of trapped flux, we show that a dipole configuration is in fact not
essential. Independent of the precise geometry of the stellar magnetosphere,
the requirement for a certain level of trapped flux predicts a definite
relationship among various CTTS observables. Moreover, superposition of
multipole stellar fields naturally yield small observed hot-spot covering
fractions and small net surface polarizations. The generalized X-wind picture
remains viable under these conditions, with the outflow from a small annulus
near the inner disk edge little affected by the modified geometry, but with
inflow highly dependent on the details of how the emergent stellar flux is
linked and trapped by the inner disk regions. Our model is consistent with
data, including recent spectropolarimetric measurements of the hot spot sizes
and field strengths in V2129 Oph and BP Tau.
