  A nested group is an increasing union of algebraic groups. It is well known
that any algebraic subgroup of the automorphism group $\mathrm{Aut}(X)$ of an
affine variety $X$ is closed with respect to the ind-topology. The closedness
of connected nested subgroups in $\mathrm{Aut}(X)$ is an open question
(Kraft--Zaidenberg'2022, arXiv:2203.11356).
  In this paper, we describe maximal nested unipotent subgroups of
$\mathrm{Aut}(X)$ by generalizing the one of triangular automorphisms of
$\mathbb{A}^n$. We show that if an abstract subgroup of $\mathrm{Aut}(X)$
consists of unipotent elements, then it is closed if and only if it is nested.
This implies that a connected nested subgroup of $\mathrm{Aut}(X)$ is closed.
  We also extend the recent description of maximal commutative unipotent
subgroups (Regeta--van Santen'2024, arXiv:2112.04784), offering a direct
construction method and relating them to our description.
