  In-plane resistivity measurements as a function of temperature and magnetic
field up to 35~T with precise orientation within the crystallographic
$ac-$plane were used to study the upper critical field, $H_{c2}$, of the
hole-doped iron-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$. Compositions
of the samples studied were spanning from underdoped $x=$0.17 ($T_c$=12~K) and
$x$=0.22 ($T_c$=20~K), both in the coexistence range of stripe magnetism and
superconductivity, though optimal doping $x$=0.39 ($T_c$=38.4~K), $x$=0.47
($T_c$=37.2~K), to overdoped $x$=0.65 ($T_c$=22~K), $x$=0.83 ($T_c$=10~K). We
find notable doping asymmetry of the shapes of the anisotropic $H_{c2}(T)$
suggesting important role of paramagnetic limiting effects in $H \parallel a$
configuration in overdoped compositions and multi-band effects in underdoped
compositions.
