UT well question is what version you aim at... guess PS3 huh?
UT99 there it started in the year 1999 (or 2000 need to chek it hehe) it has quite a long history like Quake III Arena it has a great ai and is a good shot 'em up... arena style if you are killed you are spawned again same for your opponent(s) you frag (kill) someone you gat a point... there are plenty of play modes like capture the flag, domination...
UT2004 is in my thinking the best pick, many various playmodes can be customised offline and played fully offline against bots the ai is great. Guess it's PC only though... not sure.
UT3 (from 2007?) might be the latest version though I could be wrong since UT2004 it the holy grail for me I didn't bothered that much to look for later games of this series... however I checked UT3 a while ago and if I remember correctly it has lesser playoptions can only be played "full" while online... so you can't customise and save your char offline you also lose your setting seems to be stored online... on the plus side nice graphic and great ai though. Checked the PC version so I'm unsure if the PS3 version is the same...
I'm sure someone with more knowledge will pop-up soonish and enlighten us with more recent info until then that's all I know and can give you.
:)