  We use the coupled cluster method to high orders of approximation in order to
calculate the ground-state phase diagram of the XXZ spin-$s$ kagome
antiferromagnet with easy-plane anisotropy, i.e. the anisotropy parameter
$\Delta$ varies between $\Delta=1$ (isotropic Heisenberg model) and $\Delta=0$
($XY$ model). We find that for the extreme quantum case $s=1/2$ the ground
state is magnetically disordered in the entire region $0 \le \Delta \le 1$. For
$s=1$ the ground state is disordered for $0.818 < \Delta \le 1$, it exhibits
$\sqrt{3}\times\sqrt{3}$ magnetic long-range order for $0.281 < \Delta <0.818$,
and $q=0$ magnetic long-range order for $0 \le \Delta < 0.281$. We confirm the
recent result of Chernyshev and Zhitomirsky (Phys. Rev. Lett. 113, 237202
(2014)) that the selection of the ground state by quantum fluctuations is
different for small $\Delta$ ($XY$ limit) and for $\Delta$ close to one
(Heisenberg limit), i.e., $q=0$ magnetic order is favored over
$\sqrt{3}\times\sqrt{3}$ for $0\le \Delta <\Delta_c$ and vice versa for
$\Delta_c < \Delta \le 1$. We calculate $\Delta_c$ as a function of the spin
quantum number $s$.
