  Using 385 fb^-1 of e^+e^- collisions at the CM energies of around 10.6 GeV
recorded by the BaBar experiment, we study the amplitudes of the singly
Cabibbo-suppressed decay D^0 --> K^- K^+ pi^0. We measure the strong phase
difference between the D0bar and D0 decays to the K^*(892)^+ K^- state to be
-35.5 +/- 1.9 (stat) +/- 2.2 (syst) degrees, and their amplitude ratio to be
0.599 +/- 0.013 (stat) +/- 0.011 (syst). We observe significant contributions
from the Kpi and K^-K^+ scalar and vector amplitudes, and analyze the moments
of the cosine of the helicity angle in these systems. We find no evidence for
charged, scalar kappa(800) state, nor for higher spin states. We also perform a
model-independent partial wave analysis of the K^-K^+ system in a limited mass
range around 1 GeV/c^2. We study several models for Kpi S-wave amplitude, and
describe which one is favored by our data.
