  In this paper we study the asymptotic and qualitative properties of least
energy radial sign-changing solutions of the fractional Brezis--Nirenberg
problem ruled by the s-laplacian, in a ball of $\mathbb{R}^n$, when $s \in
(0,1)$ and $n > 6s$. As usual, $\lambda$ is the (positive) parameter in the
linear part in $u$, and we consider $\lambda$ close to zero. We prove that if
such solutions vanish at the center of the ball then they vanish everywhere, we
establish a bound on the number of sign-changes and, when $s$ is close to $1$,
for a suitable value of the parameter $\lambda$ such solutions change sign
exactly once. Moreover, for any $s \in (0,1)$ and $\lambda$ sufficiently small
we prove that the number of connected components of the complement of the nodal
set corresponds to the number of sign-changes plus one. In addition, for any $s
\in (\frac{1}{2},1)$, we prove that least energy nodal solutions which change
sign exactly once have the limit profile of a "tower of bubbles", as $\lambda
\to 0^+$, i.e. the positive and negative parts concentrate at the same point
(which is the center of the ball) with different concentration speeds.
