  The triply heavy baryons are very different in their mass. They are
essentially $\Omega_{ccc}$, $\Omega_{ccb}$, $\Omega_{cbb}$ and $\Omega_{bbb}$
baryons which may be produced in a $c$ or a $b$ quark fragmentation. Here we
briefly review the direct fragmentation production of these states and choose
$\Omega_{ccc}$ and $\Omega_{bbb}$ baryons as prototype of them to consider
their production at the hadron colliders with different $\sqrt{s}$. It becomes
clear that their production cross sections fall within a rather diverse range
according to $\sqrt{s}$, minimum transverse momentum and rapidity. We present
and compare transverse momentum distributions of the differential cross
sections, $p_T^{\rm min}$ distributions of total cross sections and the
integrated total cross sections for all triply heavy baryons at CERN LHC and
simlar quantities for $\Omega_{ccc}$ and $\Omega_{bbb}$ at RHIC, Tevatron Run
II and the CERN LHC. While some of them possess considerable event rates even
at RHIC proton-proton collider, others need much more energetic hadron collider
with appropriate kinematical cuts to be produced.
