  $K^-$ optical potentials relevant to calculations of $K^-$ nuclear
quasi-bound states were developed within several chiral meson-baryon
coupled-channel interaction models. The applied models yield quite different
$K^-$ binding energies and widths. Then, the $K^-$ multinucleon interactions
were incorporated by a phenomenological optical potential fitted recently to
kaonic atom data. Though the applied $K^-$ interaction models differ
significantly in the $K^-N$ subthreshold region, our self-consistent
calculations of kaonic nuclei across the periodic table lead to conclusions
valid quite generally. Due to $K^-$ multinucleon absorption in the nuclear
medium the calculated widths of $K^-$ nuclear states are sizable, $\Gamma_{K^-}
\geq 90$ MeV, and exceed substantially their binding energies in all considered
nuclei.
