  Cosmogenic radio-nuclei are an important source of background for low-energy
neutrino experiments. In Borexino, cosmogenic $^{11}$C decays outnumber solar
$pep$ and CNO neutrino events by about ten to one. Highly efficient
identification of this background is mandatory for these neutrino analyses. We
present here the details of the most consolidated strategy, used throughout
Borexino solar neutrino measurements. It hinges upon finding the space-time
correlations between $^{11}$C decays, the preceding parent muons and the
accompanying neutrons. This article describes the working principles and
evaluates the performance of this Three-Fold Coincidence (TFC) technique in its
two current implementations: a hard-cut and a likelihood-based approach. Both
show stable performances throughout Borexino Phases II (2012-2016) and III
(2016-2020) data sets, with a $^{11}$C tagging efficiency of $\sim$90 % and
$\sim$63-66 % of the exposure surviving the tagging. We present also a novel
technique that targets specifically $^{11}$C produced in high-multiplicity
during major spallation events. Such $^{11}$C appear as a burst of events,
whose space-time correlation can be exploited. Burst identification can be
combined with the TFC to obtain about the same tagging efficiency of $\sim$90 %
but with a higher fraction of the exposure surviving, in the range of
$\sim$66-68 %.
