  We introduce the notion of Hom-co-represention and low-dimensional chain
complex. We study universal central extensions of Hom-preLie algebras and
generlize some classical results. As the same time, we introduce
$\alpha$-central extensions, universal $\alpha$-central extensions and
$\alpha$-perfect Hom-preLie algebras. We construct universal ($\alpha$)-central
extensions of Hom-preLie algebras.
