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We study the processes $\gamma \gamma \to K^+ K^- \eta$ and $\gamma \gamma\to K^+ K^- \pi^0$ using a data sample of 519 $fb^{-1}$ recorded with the BaBardetector operating at the SLAC PEP-II asymmetric-energy $e^+ e^-$ collider atcenter-of-mass energies at and near the $\Upsilon(nS)$ ($n = 2,3,4$)resonances. We observe $\eta_c \to K^+ K^- \eta$ and $\eta_c \to K^+ K^- \pi^0$decays, measure their relative branching fraction, and perform a Dalitz plotanalysis for each decay. We observe the $K^*_0(1430) \to K \eta$ decay andmeasure its branching fraction relative to the $K \pi$ decay mode to be ${\calR}(K^*_0(1430)) = \frac{{\cal B}(K^*_0(1430) \to K \eta)}{{\cal B}(K^*_0(1430)\to K \pi)} = 0.092 \pm 0.025^{+0.010}_{-0.025}$. The $\eta_c \to K^+ K^- \eta$and $K^*_0(1430) \to K \eta$ results correspond to the first observations ofthese channels. The data also show evidence for $\eta_c(2S) \to K^+ K^- \pi^0$and first evidence for $\eta_c(2S) \to K^+ K^- \eta$.

Dalitz plot analysis of $\eta_c \to K^+ K^- \eta$ and $\eta_c \to K^+ K^- \pi^0$ in two-photon interactions