  Let $G$ be a simple complex algebraic group, $P$ a parabolic subgroup of $G$
and $N$ the unipotent radical of $P.$ The so-called equivariant
compactification of $N$ by $G/P$ is given by an action of $N$ on $G/P$ with a
dense open orbit isomorphic to $N$. In this article, we investigate how many
such equivariant compactifications there exist. Our result says that there is a
unique equivariant compactification of $N$ by $G/P$, up to isomorphism, except
$\P^n$.
