  The triply heavy baryons have a rather diverse mass range. While some of them
possess considerable production rates at existing facilities, others need to be
produced at future high energy colliders. Here we study the direct
fragmentation production of the$\Omega_{ccc}$ and $\Omega_{bbb}$ baryons as the
prototypes of triply heavy baryons at the hadron colliders with different
$\sqrt{s}$. We present and compare the transverse momentum distributions of the
differential cross sections, $p_T^{\rm min}$ distributions of total cross
sections and the integrated total cross sections of these states at the RHIC,
the Tevatron Run II and the CERN LHC.
