  Let $1\le p\le\infty$. A Banach lattice $X$ is said to be $p$-disjointly
homogeneous or $(p-DH)$ (resp. restricted $(p-DH)$) if every normalized
disjoint sequence in $X$ (resp. every normalized sequence of characteristic
functions of disjoint subsets) contains a subsequence equivalent in $X$ to the
unit vector basis of $\ell_p$. We revisit $DH$-properties of Orlicz spaces and
refine some previous results of this topic, showing that $(p-DH)$-property is
not stable in the class of Orlicz spaces and the classes of restricted $(p-DH)$
and $(p-DH)$ Orlicz spaces are different. Moreover, we give a characterization
of uniform $(p-DH)$ Orlicz spaces and establish also closed connections between
this property and the duality of $DH$-property.
