We report the results from a systematic search for molecular (OH-119 um) outflows with Herschel-PACS in a sample of 43 nearby (z 11.8 +/- 0.3]. The quasars in these systems play a dominant role in driving the molecular outflows. In contrast, the most AGN dominated systems, where OH is seen purely in emission, show relatively modest OH line widths, despite their large AGN luminosities, perhaps indicating that molecular outflows subside once the quasar has cleared a path through the obscuring material. ; Comment: 49 pages, 13 figures, 4 tables; ApJ now accepted (no changes were made to the previous version)