  The main goal of this paper is to introduce the notion of $3$-L-dendriform
algebras which are the dendriform version of $3$-pre-Lie algebras. In fact they
are the algebraic structures behind the $\mathcal{O}$-operator of $3$-pre-Lie
algebras. They can be also regarded as the ternary analogous of L-dendriform
algebras. Moreover, we study the generalized derivations of $3$-L-dendriform
algebras. Finally, we explore the spaces of quasi-derivations, the centroids
and the quasi-centroids and give some properties.
