  We have carried out 200,000 N-body simulations of three identical stellar
embryos with masses from a Chabrier IMF and embedded in a molecular core. The
bodies are initially non-hierarchical and undergo chaotic motions, while
accreting using Bondi-Hoyle accretion. The coupling of dynamics and accretion
often leads to one or two dominant bodies controlling the center of the cloud
core, while banishing the other(s) to the lower-density outskirts, leading to
stunted growth. Eventually each system transforms either to a bound
hierarchical configuration or breaks apart into separate single and binary
components. The orbital motion is followed for 100 Myr. To illustrate the
simulations we introduce the 'triple diagnostic diagram', which plots two
dimensionless numbers against each other, representing the binary mass ratio
and the mass ratio of the third body to the total system mass. Numerous
freefloating BD binaries are formed in these simulations. The separation
distribution function is in good correspondence with observations, showing a
steep rise at close separations, peaking around 13 AU and then declining more
gently. Unresolved BD triple systems may appear as wider BD binaries. Mass
ratios are strongly peaked towards unity, as observed, but this is partially
due to the initial assumptions. Eccentricities gradually increase towards
higher values, due to the lack of viscous interactions in the simulations,
which would both shrink the orbits and decrease their eccentricities. The main
threat to newly born triple systems is internal instabilities, not external
perturbations. Dynamical interactions in newborn triple systems of stellar
embryos embedded in and accreting from a cloud core naturally form a population
of freefloating BD binaries, and this mechanism may constitute a significant
pathway for the formation of BD binaries. (Abstract abbreviated).
