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.
