  We study splitting and joining interactions of giant gravitons with angular
momenta $N^{1/2}\ll J\ll N$ in the type IIB string theory on $AdS_5 \times S^5$
by describing them as instantons in the tiny graviton matrix model introduced
by Sheikh-Jabbari. At large $J$ the instanton equation can be mapped to the
four-dimensional Laplace equation and the Coulomb potential for $m$ point
charges in an $n$-sheeted Riemann space corresponds to the $m$-to-$n$
interaction process of giant gravitons. These instantons provide the
holographic dual of correlators of all semi-heavy operators and the instanton
amplitudes exactly agree with the pp-wave limit of Schur polynomial correlators
in ${\cal N}=4$ SYM computed by Corley, Jevicki and Ramgoolam.
  By making a slight change of variables the same instanton equation is
mathematically transformed into the Basu-Harvey equation which describes the
system of M$2$-branes ending on M$5$-branes. As it turns out, the solutions to
the sourceless Laplace equation on an $n$-sheeted Riemann space correspond to
$n$ M5-branes connected by M2-branes and we find general solutions representing
M2-branes ending on multiple M5-branes. Among other solutions, the $n=3$ case
describes an M2-branes junction ending on three M5-branes. The effective theory
on the moduli space of our solutions might shed light on the low energy
effective theory of multiple M5-branes.
