Pebble flux Ṁ_peb as a function of time using the time-dependent protoplanetary disc evolution model (solid red line) and for a protoplanetary disc evolution model where the outer gas disc does not evolve in time (dotted red line). In blue we show constant pebble fluxes of 45 M_E/Myr (solid line) and 270 M_E/Myr (dotted line). In principle, a pebble flux of 45 M_E/Myr is large enough to grow a planet from 5 to 10 M_E in 1 Myr, but the migration timescale is a factor of a few shorter than that, indicating that planet would be lost to the central star. Higher pebble fluxes of ≈270 M_E/Myr allow growth fast enough to reach the pebble isolation mass and thus allow gas accretion and the transition to type-II migration before type-I migration drives the planet all the way to the central star. Our revised disc evolution model is able to reproduce these high pebble fluxes (dotted red line).