  Large high-quality single crystals of hole-doped iron-based superconductor
(Ba$_{1-x}$K$_x$)Fe$_2$As$_2$ were grown over a broad composition range $0.22
\leq x \leq 1$ by inverted temperature gradient method. We found that high
soaking temperature, fast cooling rate, and adjusted temperature window of the
growth are necessary to obtain single crystals of heavily K doped crystals
(0.65$\leq x \leq$ 0.92) with narrow compositional distributions as revealed by
sharp superconducting transitions in magnetization measurements and close to
100% superconducting volume fraction. The crystals were extensively
characterized by x-ray and compositional analysis, revealing monotonic
evolution of the $c$-axis crystal lattice parameter with K substitution.
Quantitative measurements of the temperature-dependent in-plane resistivity,
$\rho(T)$ found doping-independent, constant within error bars, resistivity at
room temperature, $\rho(300K)$, in sharp contrast with significant doping
dependence in electron and isovalent substituted BaFe$_2$As$_2$ based
compositions. The shape of the temperature dependent resistivity, $\rho(T)$,
shows systematic doping-evolution, being close to $T^2$ in overdoped and
revealing significant contribution of the $T$-linear component at optimum
doping. The slope of the upper critical field, $d H_{c2}/dT$, scales linearly
with $T_c$ for both $H\parallel c$, $ H_{c2,c}$, and $H \parallel ab$,
$H_{c2,ab}$. The anisotropy of the upper critical field, $\gamma \equiv
H_{c2,ab} / H_{c2,c}$ determined near zero-field $T_c$ increases from $\sim$2
to 4-5 with increasing K doping level from optimal $x \sim$0.4 to strongly
overdoped $x$=1.
