  This paper is concerned with the ground states of a coupled
pseudo-relativistic Hartree system in $\mathbb{R} ^{3} $ with trapping
potentials, where the intraspecies and the interspecies interaction are both
attractive. By investigating an associated constraint minimization problem, the
existence and non-existence of ground states are classified completely. Under
certain conditions on the trapping potentials, we present a precise analysis on
the concentration behavior of the minimizers as the coupling coefficient goes
to a critical value, where the minimizers blow up and the maximum point
sequence concentrates at a global minima of the associated trapping potentials.
We also identify an optimal blowing up rate under polynomial potentials by
establishing some delicate estimates of energy functionals.
