  We study the energy transfer process in quantum battery systems consisting of
multiple central spins and bath spins. Here with "quantum battery" we refer to
the central spins, whereas the bath serves as the "charger". For the single
central-spin battery, we analytically derive the time evolutions of the energy
transfer and the charging power with arbitrary number of bath spins. For the
case of multiple central spins in the battery, we find the scaling-law relation
between the maximum power $P_{max}$ and the number of central spins $N_B$. It
approximately satisfies a scaling law relation $P_{max}\propto N_{B}^{\alpha}$,
where scaling exponent $\alpha$ varies with the bath spin number $N$ from the
lower bound $\alpha =1/2$ to the upper bound $\alpha =3/2$. The lower and upper
bounds correspond to the limits $N\to 1$ and $N\gg N_B$, respectively. In
thermodynamic limit, by applying the Holstein-Primakoff (H-P) transformation,
we rigorously prove that the upper bound is $P_{max}=0.72 B A \sqrt{N}
N_{B}^{3/2}$, which shows the same advantage in scaling of a recent charging
protocol based on the Tavis-Cummins model. Here $B$ and $A $ are the external
magnetic field and coupling constant between the battery and the charger.
