iPad syncs only one direction

I use three iPhones and one iPad. Only the iPad now has problems. (none of which are jailbroken)

I can sync anything by using iTunes app on Mac to install. It always works properly in that direction. However, if I delete any app from the iPad home screen or add any app from the iPad App Store - a sync to the Mac (wired or Wifi) will simply re-add the apps deleted or wipe out the apps added. Even if I've Transferred apps first, before syncing.

After a full Erase all Contents and Restore as new device (not from backup), as well as erasing all iTunes backups of this iPad and iCloud backups - no changes.

I've backed up to Mac and to iCloud, synced not Wifi and with Wifi. I've repaired permissions as well. Applied new iTunes (iBooks textbooks) update, still no fix in sight.

Any thoughts? I'm at a loss here..

thanks