  We consider the nonlocal Liouville type equation $$ (-\Delta)^{\frac{1}{2}} u
= \varepsilon \kappa(x) e^u, \quad u > 0, \quad \mbox{in } I, \qquad u = 0,
\quad \mbox{in } \mathbb{R} \setminus I, $$ where $I$ is a union of $d \geq 2$
disjoint bounded intervals, $\kappa$ is a smooth bounded function with positive
infimum and $\varepsilon > 0$ is a small parameter. For any integer $1 \leq m
\leq d$, we construct a family of solutions $(u_\varepsilon)_{\varepsilon}$
which blow up at $m$ interior distinct points of $I$ and for which $\varepsilon
\int_I \kappa e^{u_\varepsilon} \, \rightarrow 2 m \pi$, as $\varepsilon \to
0$. Moreover, we show that, when $d = 2$ and $m$ is suitably large, no such
construction is possible.
