  Formation of bodies near the deuterium-burning limit is considered by
detailed numerical simulations according to the core-nucleated giant planet
accretion scenario. The objects, with heavy-element cores in the range 5-30
Mearth, are assumed to accrete gas up to final masses of 10-15 Jupiter masses
(Mjup). After the formation process, which lasts 1-5 Myr and which ends with a
'cold-start', low-entropy configuration, the bodies evolve at constant mass up
to an age of several Gyr. Deuterium burning via proton capture is included in
the calculation, and we determined the mass, M50, above which more than 50% of
the initial deuterium is burned. This often-quoted borderline between giant
planets and brown dwarfs is found to depend only slightly on parameters, such
as core mass, stellar mass, formation location, solid surface density in the
protoplanetary disk, disk viscosity, and dust opacity. The values for M50 fall
in the range 11.6-13.6 Mjup, in agreement with previous determinations that do
not take the formation process into account. For a given opacity law during the
formation process, objects with higher core masses form more quickly. The
result is higher entropy in the envelope at the completion of accretion,
yielding lower values of M50. For masses above M50, during the
deuterium-burning phase, objects expand and increase in luminosity by 1 to 3
orders of magnitude. Evolutionary tracks in the luminosity-versus-time diagram
are compared with the observed position of the companion to Beta Pictoris.
