  In this paper we study half-BPS type IIB supergravity solutions with multiple
$AdS_3\times S^3\times M_4$ asymptotic regions, where $M_4$ is either $T^4$ or
$K_3$. These solutions were first constructed in [1] and have geometries given
by the warped product of $AdS_2 \times S^2 \times M_4 $ over $\Sigma$, where
$\Sigma$ is a Riemann surface. We show that the holographic boundary has the
structure of a star graph, i.e. $n$ half-lines joined at a point. The attractor
mechanism and the relation of the solutions to junctions of self-dual strings
in six-dimensional supergravity are discussed. The solutions of [1] are
constructed introducing two meromorphic and two harmonic functions defined on
$\Sigma$. We focus our analysis on solutions corresponding to junctions of
three different conformal field theories and show that the conditions for
having a solution charged only under Ramond-Ramond three-form fields reduce to
relations involving the positions of the poles and the residues of the relevant
harmonic and meromorphic functions. The degeneration limit in which some of the
poles collide is analyzed in detail. Finally, we calculate the holographic
boundary entropy for a junction of three CFTs and obtain a simple expression in
terms of poles and residues.
