The annihilation channel ppBAR --> omegapi0pi0, where omega decays to
pi0gamma, was studied with antiprotons stopped in liquid hydrogen. Thi
s reaction is dominated by the production of b1(0)(1235) with contribu
tions from f2(1270) and the pipi S-wave. The branching ratio for ppBAR
--> omegapi0pi0 is (2.00 +/- 0.21)% of all annihilations. The branchi
ng ratios for b1(0)(1235)pi0 (b1 --> omegapi0) and f2(1270)omega (f2 -
-> pi0pi0) are (0.92 +/- 0.11)% and (0.57 +/- 0.07)% of all annihilati
ons, respectively. Upper limits for the production of vector mesons de
caying to omegapi are given and the pipi mass distribution around 1 Ge
V is discussed.