  We study quantitative aspects and concentration phenomena for ground states
of the following nonlocal Schr\"odinger equation $
  (-\Delta)^s u+V(x)u= u^{2_s^*-1-\varepsilon} \ \
  \text{in}\ \ \mathbb{R}^N, $ where $\varepsilon>0$, $s\in (0,1)$,
$2^*_s:=\frac{2N}{N-2s}$, $N>4s$. We show that the ground state
$u_{\varepsilon}$ blows up and precisely with the following rate
$\|u_{\varepsilon}\|_{L^\infty(\mathbb{R}^N)}\sim
\varepsilon^{-\frac{N-2s}{4s}}$, as $\epsilon\rightarrow 0^+$. We also localize
the concentration points and, in the case of radial potentials $V$, we prove
local uniqueness of sequences of ground states which exhibit a concentrating
behavior.
