  The purpose of this paper is to present several examples of non--autonomous
basins of attraction that arise from sequences of automorphisms of $\mathbb
C^k$. In the first part, we prove that the non-autonomous basin of attraction
arising from a pair of automorphisms of $\mathbb C^2$ of a prescribed form is
biholomorphic to $\mathbb C^2$. This, in particular, provides a partial answer
to a question raised in connection with Bedford's Conjecture about uniformizing
stable manifolds. In the second part, we describe three examples of Short
$\mathbb C^k$'s with specified properties. First, we show that for $k \geq 3$,
there exist $(k-1)$ mutually disjoint Short $\mathbb C^k$'s in $\mathbb C^k$.
Second, we construct a Short $\mathbb C^k$, large enough to accommodate a
Fatou-Bieberbach domain, that avoids a given algebraic variety of codimension
$2$. Lastly, we discuss examples of Short $\mathbb C^k$'s with (piece-wise)
smooth boundaries.
