I have a Powerbook G4 10.5.8 and Time Machine has been deleted.

Hello, I suggest you do this first...

Safe Boot, (holding Shift key down at bootup), run Disk Utility in Applications>Utilities, then highlight your drive, click on Repair Permissions, reboot when it completes.

(Safe boot may stay on the gray radian for a long time, let it go, it's trying to repair the Hard Drive & clear caches.)

Then re-apply the big combo update...

Repair Permissions twice in a row afterwords, reboot.

1058 Combo Update, 10.5.8...

http://support.apple.com/downloads/Mac_OS_X_10_5_8_Combo_Update

Hmmm, it should be, it's part of the combo installer...

This was viewed with Pacifist...

http://www.charlessoft.com/

Did you download the Combo Update and then install it?

Hmmm, I don't think so, but...

Get Pacifist...

http://www.charlessoft.com/

then extract/install what you need from the Combo.

Find Any File...

http://apps.tempel.org/FindAnyFile/

Hold Option or alt key when selecting Find to Find All.

Search for Name Contains... time machine

Great news, thanks! 🙂

Which one was it that did it?

Thanks for the report. 🙂