We study the transport pathways from the top of convective clouds to the lower tropical stratosphere during the Asian monsoon, using a dense cover of Lagrangian trajectories driven by observed clouds and the two reanalyses ERA-Interim and ERA5 with diabatic and kinematic vertical motions. We find that the upward propagation of convective impact is very similar for the kinematic and diabatic trajectories using ERA5, while the two cases strongly differ for ERA-Interim. The parcels that stay confined within the Asian monsoon anticyclone and reach 380 K are mostly of continental origin, while maritime sources dominate when the whole global 380 K surface is considered. Over the continent, the separation of descending and ascending motion occurs at a crossover level near 364 K, which is slightly above the clear-sky zero level of radiative heating rate, except over the Tibetan Plateau. The strong impact of the Tibetan Plateau with respect to its share of high clouds is entirely due to its elevated proportion of high clouds above the crossover. The vertical conduit found in previous studies actually ends where the convective clouds detrain. Subsequent parcel motion is characterized by an ascending spiral that spans the whole anticyclone. The mean age of parcels with respect to convection exhibits a minimum at the centre of the Asian monsoon anticyclone, due to the permanent renewal by fresh convective air, and largest values on the periphery as air spirals out. This contrast is reduced by dilution for increasing altitude. Above 360 K, the confinement can be represented by a simple 1-D process of diabatic advection with loss. The mean loss time is about 13 d and uniform over the range 360 to 420 K, which is compared with a total circulation time of 2 to 3 weeks around the anticyclone. The vertical dilution is consequently exponential with an e-folding potential temperature scale of 15 K (about 3 km). The mechanism is compatible with the appearance of a columnar tracer pattern within the anticyclone. It is noticeable that the tropopause does not exhibit any discontinuity in the transport properties when seen in terms of potential temperature.