All the posts seem to indicate problems, but they are pretty old. Anyone have it working?
as of yesterday I do have it working! 
Thanks. I would appreciate feedback as to what is working and how it is working and any specific steps you had to take in addition to a basic install to get it working. Are you running a dual boot with OS X?
Sorry for the late reply @ling_mate. After getting it to boot and run, my system kept freezing. It took me a great deal of research and t&e to figure it out.
I finally went ahead and did a re-install after sidestepping to OpenBSD. In the end I got Ubuntu Mate 16.04 LTS up and running. I installed from a USB through Open Firmware. My USB was [ usb1 ] on [ /usb@1 /disk@1 ].
I booted with the command: [ boot usb1/disk@1:2,\yaboot ]
Once it was booted, I typed the live-command: [ live-nosplash-powerpc radeon.agpmode=-1 ] to boot into linux live and turn radeon kms off.
Next I installed Ubuntu Mate using the entire harddisk. I had the Ethernet-cable hooked up, so I went ahead and had the install look for updated firmware drivers and additional packages needed for my hardware.
After installation, I made things final using nano-editor in terminal to edit my yaboot.conf file adding: [ radeon.modeset=0 radeon.agpmode=-1 radeonfb=1024x768-32 ] to it. After saving I rand the command: [ sudo ybin -v ] and rebooted.
Ever since, the the G4 has been running without a glitch.
However, I am looking for minimum system imprint, so I'm going to ditch the Mate desktop environment and switch to icewm desktop environment. Also Firefox will have to go, since it's eating up too many resources. I'm considering Arctic Fox browser.
I hope this helps you out getting Ubuntu Mate running on G4-architecture.
Note: I'm running on a 2005 Apple iBook G4 7447a @ 1.42GHz with 1GB DDR-333 RAM and 60 GB ATA-100 HDD.