  For a poset whose Hasse diagram is a rooted plane forest $F$, we consider the
corresponding tree descent polynomial $A_F(q)$, which is a generating function
of the number of descents of the labelings of $F$. When the forest is a path,
$A_F(q)$ specializes to the classical Eulerian polynomial. We prove that the
coefficient sequence of $A_F(q)$ is unimodal and that if $\{T_{n}\}$ is a
sequence of trees with $|T_{n}| = n$ and maximal down degree $D_{n} =
O(n^{0.5-\epsilon})$ then the number of descents in a labeling of $T_{n}$ is
asymptotically normal.
