  We introduce Hom-actions, semi-direct product and establish the equivalence
between split extensions and the semi-direct product extension of Hom-Leibniz
algebras. We analyze the functorial properties of the universal
({\alpha})-central extensions of ({\alpha})-perfect Hom-Leibniz algebras. We
establish under what conditions an automorphism or a derivation can be lifted
in an {\alpha}-cover and we analyze the universal {\alpha}-central extension of
the semi-direct product of two {\alpha}-perfect Hom-Leibniz algebras.
