  We analyze the consequences of the recently found generalization of the
Christodoulou-Ruffini black hole mass decomposition for Einstein-Born-Infeld
black holes [characterized by the parameters $(Q,M,b)$, where $M =
M(M_{irr},Q,b)$, $b$ scale field, $Q$ charge, $M_{irr}$ "irreducible mass",
physically meaning the energy of a black hole when its charge is null] and
their interactions. We show in this context that their description is largely
simplified and can basically be split into two families depending upon the
parameter $b|Q|$. If $b|Q|\leq 1/2$, then black holes could have even zero
irreducible masses and they always exhibit single, non degenerated, horizons.
If $b|Q|>1/2$, then an associated black hole must have a minimum irreducible
mass (related to its minimum energy) and has two horizons up to a transitional
irreducible mass. For larger irreducible masses, single horizon structures
raise again. By assuming that black holes emit thermal uncharged scalar
particles, we further show in light of the black hole mass decomposition that
one satisfying $b|Q|>1/2$ takes an infinite amount of time to reach the zero
temperature, settling down exactly at its minimum energy. Finally, we argue
that depending on the fundamental parameter $b$, the radiation (electromagnetic
and gravitational) coming from Einstein-Born-Infeld black holes could differ
significantly from Einstein-Maxwell ones. Hence, it could be used to assess
such a parameter.
