  We explore the growth of planetary embryos by planetesimal accretion up to
and beyond the point where pebble accretion becomes efficient at the so-called
Hill-transition mass. Both the transition mass and the characteristic mass of
planetesimals formed by the streaming instability increase with increasing
distance from the star. We developed a model for the growth of a large
planetesimal (embryo) embedded in a population of smaller planetesimals formed
in a filament by the streaming instability. The model includes in a
self-consistent way the collisional mass growth of the embryo, the
fragmentation of the planetesimals, the velocity evolution of all involved
bodies, as well as the viscous spreading of the filament. We find that the
embryo accretes all available material in the filament during the lifetime of
the protoplanetary disc only in the inner regions of the disc. In contrast, we
find little or no growth in the outer parts of the disc beyond 5--10 AU.
Overall, our results demonstrate very long timescales for collisional growth of
planetesimals in the regions of the protoplanetary disc where giant planets
form. As such, in order to form giant planets in cold orbits, pebble accretion
must act directly on the largest bodies present in the initial mass-function of
planetesimals with little or no help from mutual collisions.
