  Using a relativized diquark model Hamiltonian, we calculate the masses of
$J^{PC}=0^{++}$ ground-state tetraquarks in the following systems: $b s \bar b
\bar s$, $bb \bar n \bar n$ ($n=u, d$), $bb \bar s \bar s$, $cc\bar c \bar c$,
$b b \bar b \bar b$, $b c\bar b \bar c$ and $b b \bar c \bar c$. We also
compute extensive spectra for the fully-heavy quark flavour combinations.
Finally, as a test of the diquark model approach, we compute the masses of
fully-heavy baryons in the diquark model. Our results may be compared soon to
the forthcoming experimental data for fully-heavy three-quark systems.
