We present data on <(p)over bar p> --> 3 pi(0) at nine ii momenta from 600 to 1940 MeV/c. This process is dominated by the f(2)(1270)pi(0) channel, where we observe I = 1 resonances with the following masses and widths: 4(++)(2260+/-15), Gamma = 180 +/- 20 MeV, 4(++)(2005 +/- 25), Gamma = 360 +/- 80 MeV, 3 (++)(2310 +/- 40), Gamma = 180(-60)(+120) MeV, 3(++)(2070 +/- 20), Gamma = 170 +/- 40 MeV, 2(++)(2280 +/- 30), Gamma = 280 +/- 50 MeV, 2(++)(2100(-30)(+10)) , Gamma = 360(-100)(+40): MeV, 1(++)(2100 +/- 20), Gamma = 300(-60)(+30) MeV, (2340 +/- 30), Gamma = 230 +/- 70 MeV. (C) 1999 Published by Elsevier Science B.V. All rights reserved.