We present time-resolved spectroscopy of the AM CVn-type binaries GP Com and V396 Hya obtained with VLT/X-Shooter and VLT/UVES. We fully resolve the narrow central components of the dominant helium lines and determine radial velocity semi-amplitudes of $K_{rm spike} = 11.7pm0.3$ km s$^{-1}$ for GP Com and $K_{rm spike} = 5.8pm0.3$ km s$^{-1}$ for V396 Hya. The mean velocities of the narrow central components show variations from line to line. Compared to calculated line profiles that include Stark broadening we are able to explain the displacements, and the appearance of forbidden helium lines, by additional Stark broadening of emission in a helium plasma with an electron density $n_esimeq 5times 10^{15}$ cm$^{-3}$. More than $30$ nitrogen and more than $10$ neon lines emission lines were detected in both systems. Additionally, $20$ nitrogen absorption lines are only seen in GP Com. The radial velocity variations of these lines show the same phase and velocity amplitude as the central helium emission components. The small semi-amplitude of the central helium emission component, the consistency of phase and amplitude with the absorption components in GP Com as well as the measured Stark effect shows that the central helium emission component, the so-called central-spike, is consistent with an origin on the accreting white dwarf. We use the dynamics of the bright spot and the central spike to constrain the binary parameters for both systems and find a donor mass of $9.6$ - $42.8$ M$_{rm Jupiter}$ for GP Com and $6.1$ - $30.5$ M$_{rm Jupiter}$ for V396 Hya. We find an upper limit for the rotational velocity of the accretor of $v_{rm rot}<46$ km s$^{-1}$ for GP Com and $v_{rm rot}<59$ km s$^{-1}$ for V396 Hya which excludes a fast rotating accretor in both systems.
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