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We report observations of the b --> d penguin-dominated decays
B+ --> K0bar K+ and B0 --> K0 K0bar in approximately
316 fb^-1 of e+e- collision data collected with the BaBar detector.
We measure the branching fractions BF(B+ --> K0bar K+) = (1.61 +/- 0.44 +/- 0.09) * 10^-6
and BF(B0 --> K0 K0bar) = (1.08 +/- 0.28 +/- 0.11) * 10^-6,
and the CP-violating charge asymmetry A_{CP}(K0bar K+) = 0.10 +/- 0.26 +/- 0.03.
Using a vertexing technique previously employed in several analyses of
all-neutral final states containing kaons,
we report the first measurement of time-dependent CP-violating asymmetries in B0 --> K0 K0bar,
obtaining S = -1.28 +0.80/-0.73 +0.11/-0.16 and
C = -0.40 +/- 0.41 +/- 0.06.
We also report improved measurements of the branching fraction
BF(B+ --> K0 pi+) = (23.9 +/- 1.1 +/- 1.0) * 10^-6
and CP-violating charge asymmetry A_{CP}(K0 pi+) = -0.029 +/- 0.039 +/- 0.010.
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