Two ways to disable OpenOffice splash screen in Ubuntu

1. Open Terminal (Applications >> Accessories >> Terminal) and type

        sudo gedit /etc/openoffice/sofficerc
       Change the value of Logo=1 to Logo=0
    Save sofficerc file.
(More: Don't forget to roam through /etc/ directory as you can change settings of OS there :-) )

2.  Open menu editor (System >> Preferences >> Main Menu) or type alacarte in Terminal.
      Find the entries of Openoffice applications, right click, click Properties.Add -nologo to existing command in Command box.

Former will disable splash screen of every OpenOffice applications you are opening and latter will disable that feature for selective applications like OpenOffice Writer.