We report the results of a study of $B^{pm}to K^{pm}eta_c$ and $B^{pm}to K^{pm}eta_c(2S)$ decays followed by $eta_c$ and $eta_c(2S)$ decays to $(K_SKpi)^0$. The results are obtained from a data sample containing 535 million $Bbar{B}$-meson pairs collected by the Belle experiment at the KEKB $e^+e^-$ collider. We measure the products of the branching fractions ${mathcal B}(B^{pm}to K^{pm}eta_c){mathcal B}(eta_cto K_S K^{pm}pi^{mp})=(26.7pm 1.4(stat)^{+2.9}_{-2.6}(syst)pm 4.9(model))times 10^{-6}$ and ${mathcal B}(B^{pm}to K^{pm}eta_c(2S)){mathcal B}(eta_c(2S)to K_S K^{pm}pi^{mp})=(3.4^{+2.2}_{-1.5}(stat+model)^{+0.5}_{-0.4} syst))times 10^{-6}$. Interference with the non-resonant component leads to significant model uncertainty in the measurement of these product branching fractions. Our analysis accounts for this interference and allows the model uncertainty to be reduced. We also obtain the following charmonia masses and widths: $M(eta_c)=(2985.4pm 1.5(stat)^{+0.5}_{-2.0}(syst))$ MeV/$c^2$, $Gamma(eta_c)=(35.1pm 3.1(stat)^{+1.0}_{-1.6}(syst))$ MeV/$c^2$, $M(eta_c(2S))=(3636.1^{+3.9}_{-4.2}(stat+model)^{+0.7}_{-2.0}(syst))$ MeV/$c^2$, $Gamma(eta_c(2S))=(6.6^{+8.4}_{-5.1}(stat+model)^{+2.6}_{-0.9}(syst))$ MeV/$c^2$.
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