  The class of (eventually) dendric words generalizes well-known families such
as the Arnoux-Rauzy words or the codings of interval exchanges. There are still
many open questions about the link between dendricity and morphisms. In this
paper, we focus on two questions. The first one is the evolution of the factor
complexity when applying a non-erasing morphism to an eventually dendric word.
We next look at the morphisms that preserve dendricity for all dendric words
and show that they are exactly those generated by the Arnoux-Rauzy morphisms.
