  EX Hya is one of the best studied, but still enigmatic intermediate polars.
We present phase-resolved blue VLT/UVES high-resolution ($\lambda/\Delta
\lambda\simeq16.000$) spectra of EX Hya taken in January 2004. Our analysis
involves a unique decomposition of the Balmer line profiles into the
spin-modulated line wings that represent streaming motions in the magnetosphere
and the orbital-phase modulated line core that represents the accretion disk.
Spectral analysis and tomography show that the division line between the two is
solidly located at $\mid\upsilon_{rad}\mid\simeq1200$ km s$^{-1}$, defining the
inner edge of the accretion disk at $r_{in}\simeq{7}\times 10^{9}$ cm or
$\sim10 R_1$ (WD radii). This large central hole allows an unimpeded view of
the tall accretion curtain at the lower pole with a shock height up to
$h_{sh}\sim1 R_1$ that is required by X-ray and optical observations. Our
results contradict models that advocate a small magnetosphere and a small inner
disk hole. Equating $r_{in}$ with the magnetospheric radius in the orbital
plane allows us to derive a magnetic moment of the WD of $\mu_1\simeq1.3\times
10^{32}$ G cm$^{3}$ and a surface field strength $B_1\sim0.35$ MG. Given a
polar field strength $B_{p} \lesssim 1.0$ MG, optical circular polarization is
not expected. With an accretion rate $\dot M = 3.9\times10^{-11}$
$M_{\odot}$yr$^{-1}$, the accretion torque is $G_{acc}\simeq 2.2 \times
10^{33}$ g cm$^{2}$s$^{-2}$. The magnetostatic torque is of similar magnitude,
suggesting that EX Hya is not far from being synchronized. We measured the
orbital radial-velocity amplitude of the WD, $K_1=58.7\pm3.9$ km s$^{-1}$, and
found a spin-dependent velocity modulation as well. The former is in perfect
agreement with the mean velocity amplitude obtained by other researchers,
confirming the published component masses $M_1\simeq0.79 M_\odot$ and
$M_2\simeq0.11 M_\odot$.
