  Let $A$ be a hereditary algebra over an algebraically closed field $k$ and
$A^{(m)}$ be the $m$-replicated algebra of $A$. Given an $A^{(m)}$-module $T$,
we denote by $\delta (T)$ the number of non isomorphic indecomposable summands
of $T$. In this paper, we prove that a partial tilting $A^{(m)}$-module $T$ is
a tilting $A^{(m)}$-module if and only if $\delta (T)=\delta (A^{(m)})$, and
that every partial tilting $A^{(m)}$-module has complements. As an application,
we deduce that the tilting quiver $\mathscr{K}_{A^{(m)}}$ of $A^{(m)}$ is
connected. Moreover, we investigate the number of complements to almost tilting
modules over duplicated algebras.
