In head-on relativistic black-hole collisions, peak recoil is about 7.4 times the final kick, independent of spin and momentum.

The collision of black holes at relativistic speeds probes gravity in its most extreme dynamical regime. While the maximum gravitational recoil from \emph{grazing} high-energy collisions ($\approx28\,562$~km/s, i.e., $\sim0.1c$) and the maximum radiated energy $E_{\rm rad}$ and remnant spin $\alpha_f^{\max}$ from such encounters ($E_{\rm rad}/M_{\rm ADM}\approx32\%$ where $M_{\rm ADM}$ is the ADM mass, and $\alpha_f^{\max}\approx0.987$) have been established previously~\cite{Healy:2022jbh,Healy:2024lhl}, here we focus on the \emph{head-on} high-energy collision of equal-mass spinning black holes and on the detailed structure of the resulting recoil. Performing a sequence of full numerical simulations for spin magnitudes $s=0.5,0.65$, and $0.8$ over a range of initial momenta $\gamma v$, we characterize the peak recoil $V_p$, the final recoil $V_f$, and the antikick $\Delta V\equiv V_f-V_p$, and we provide phenomenological fits of their dependence on $\gamma v$ and $s$. We complement these results with a zero-frequency-limit (ZFL) analysis of the radiated energy and momentum, a quasinormal-mode model of the antikick, and a superposed boosted double-Kerr close-limit estimate. We find that in the relativistic regime ($\gamma v>1$) the peak and final recoil are directly proportional, $V_p\approx7.4\,V_f$ (equivalently $\Delta V \approx-6.4\,V_f$), largely independent of both the initial momentum and the spin magnitude, pointing to a common post-merger relaxation. While the ZFL predicts a leading linear-in-spin dependence, the close-limit analysis predicts a leading $s^3$ dependence of the recoil amplitude; with the three spin magnitudes studied here the empirical exponent is $s^{1.27\pm0.08}$, motivating an even higher energy collision spin sequence study.