  We conduct a first-principles study of Hall effects in rare-earth
dichalcogenides, focusing on monolayers of the H-phase EuX$_2$ and GdX$_2$,
where X = S, Se, and Te. Our predictions reveal that all EuX$_2$ and GdX$_2$
systems exhibit high magnetic moments and wide bandgaps. We observe that while
in case of EuX$_2$ the $p$ and $f$ states hybridize directly below the Fermi
energy, the absence of $f$ and $d$ states of Gd at the Fermi energy results in
$p$-like spin-polarized electronic structure of GdX$_2$, which mediates
$p$-based magnetotransport. Notably, these systems display significant
anomalous, spin, and orbital Hall conductivities. We find that in GdX$_2$ the
strength of correlations controls the relative position of $p$, $d$ and
$f$-states and their hybridization which has a crucial impact on $p$-state
polarization and the anomalous Hall effect, but not the spin and orbital Hall
effect. Moreover, we find that the application of strain can significantly
modify the electronic structure of the monolayers, resulting in quantized
charge, spin and orbital transport in GdTe$_2$ via a strain-mediated orbital
inversion mechanism taking place at the Fermi energy. Our findings suggest that
rare-earth dichalcogenides hold promise as a platform for topological
spintronics and orbitronics.
