  We study $U(1)$ gauged gravitating compact $Q$-ball, $Q$-shell solutions in a
nonlinear sigma model with the target space $\mathbb{C}P^N$. The models with
odd integer $N$ and a special potential can be parameterized by $N$-th complex
scalar fields and they support compact solutions. Implementing the $U(1)$ gauge
field in the model, the behavior of the solutions become complicated than the
global model. Especially, they exhibit branch, i.e., two independent solutions
with same shooting parameter. The energy of the solutions in the first branch
behaves as $E\sim Q^{5/6}$ for small $Q$, where $Q$ stands for the $U(1)$
Noether charge. For the large $Q$, it gradually deviates from the scaling
$E\sim Q^{5/6}$ and, for the $Q$-shells it is $E\sim Q^{7/6}$, which forms the
second branch. A coupling with gravity allows for harboring of the
Schwarzschild black holes for the $Q$-shell solutions, forming the charged
boson shells. The space-time then consist of a charged black hole in the
interior of the shell, surrounded by a $Q$-shell, and the outside becomes a
Reissner-Nordstr\"om space-time. These solutions inherit the scaling behavior
of the flat space-time.
