Using a relativized diquark model Hamiltonian, we calculate the masses of $$J^{PC}=0^{++}$$
J
PC
=
0
+
+
ground-state tetraquarks in the following systems: $$b s {\bar{b}} {\bar{s}}$$
b
s
b
¯
s
¯
, $$bb {\bar{n}} {\bar{n}}$$
b
b
n
¯
n
¯
($$n=u, d$$
n
=
u
,
d
), $$bb {\bar{s}} {\bar{s}}$$
b
b
s
¯
s
¯
, $$cc{\bar{c}} {\bar{c}}$$
c
c
c
¯
c
¯
, $$b b {\bar{b}} {\bar{b}}$$
b
b
b
¯
b
¯
, $$b c{\bar{b}} {\bar{c}}$$
b
c
b
¯
c
¯
and $$b b {\bar{c}} {\bar{c}}$$
b
b
c
¯
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.