  Aims : We re-examine the conditions required to steadily deviate an accretion
flow from a circumstellar disc into a magnetospheric funnel flow onto a slow
rotating young forming star. Methods : New analytical constraints on the
formation of accretion funnels flows due to the presence of a dipolar stellar
magnetic field disrupting the disc are derived. The Versatile Advection Code is
used to confirm these constraints numerically. Axisymmetric MHD simulations are
performed, where a stellar dipole field enters the resistive accretion disc,
whose structure is self-consistently computed. Results : The analytical
criterion derived allows to predict a priori the position of the truncation
radius from a non perturbative accretion disc model. Accretion funnels are
found to be robust features which occur below the co-rotation radius, where the
stellar poloidal magnetic pressure becomes both at equipartition with the disc
thermal pressure and is comparable to the disc poloidal ram pressure. We
confirm the results of Romanova et al. 2002 and find accretion funnels for
stellar dipole fields as low as 140 G in the low accretion rate limit of
$10^{-9} M_\odot.yr^{-1}$. With our present numerical setup with no disc
magnetic field, we found no evidence of winds, neither disc driven nor X-winds,
and the star is only spun up by its interaction with the disc. Conclusions :
Weak dipole fields, similar in magnitude to those observed, lead to the
development of accretion funnel flows in weakly accreting T Tauri stars.
However, the higher accretion observed for most T Tauri stars (${\dot M} \sim
10^{-8} M_\odot.yr^{-1}$) requires either larger stellar field strength and/or
different magnetic topologies to allow for magnetospheric accretion.
