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, ApJ, 578, 420) and find accretion funnels for stellar dipole fields as low as 140 G in the low accretion rate limit of 10 −9 M 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 (Ṁ ∼ 10 −8 M yr −1 ) requires either larger stellar field strength and/or different magnetic topologies to allow for magnetospheric accretion.

We study the influence of stratification on stellar turbulent convection near the stellar surface and in depth by carrying out 3D high resolution hydrodynamic simulations with the ASH code. Four simulations with different radial density contrast corresponding to different aspect ratio for the same underlying 4 Myr 0.7M ⊙ pre-main sequence star model are thus performed. We highlight the existence of giant cells which are embedded in the complex surface convective patterns using a wavelet and time correlation analysis. Next, we study their properties such as their lifetime, aspect ratio and spatial extension in the different models both in latitude and depth according to the density contrast. We find that these giants cells have a lifetime larger than the stellar period with a typical longitudinal width of 490 Mm and a latitudinal extension increasing with the radial density contrast overpassing 50 • of latitude for the thickest convective zone. Their rotation rate is much larger than the local differential rotation rate increasing also with the radial density contrast. However, their spatial coherence as a function of depth decrease with the density contrast due to the stronger shear present in these more stratified cases.