Avivo HD isn't existent.

It looks like it is in a seperate Avivo package. I think these may be for 10.6 version of CCC. At least their version of it is 10.6:

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Avivo™ Package 29.2 MB 10.6 6/16/2010
Description:
Package Includes:
Encoder
Parental Control
Visual C++ Patch
Avivo Video Converter


Avivo Package Download

or

Download

No mention of 3GP support though, at least on older versions. Changelog for 10.6 doesn't mention any added video formats though:

ATI Avivo Video Converter

ATI has also released a transcoder software dubbed "ATI Avivo Video Converter," which supports transcoding between H.264, VC-1, WMV9, WMV9 PMC, MPEG-2, MPEG-4, DivX video formats, as well as formats used in iPod and PSP. Earlier versions of this software uses only the CPU for transcoding, but have been locked for exclusive use with the ATI X1000 series of GPUs. Software modifications have made it possible to use version 1.12 of converter on a wider range of graphics adapters . The ATI Avivo Video Converter for Windows Vista was available with the release of Catalyst 7.9 (September 2007 release, version 8.411).

The ATI Avivo Video Converter with GPU transcoding acceleration is now also available for use with HD 4800 and HD 4600 series graphics cards and is included with the Catalyst 8.12 drivers. Support for Vista x64 is available via a separate download starting with Catalyst 9.6 (9-6_vista32-64_xcode). The new software is faster than Badaboom, an encoder that uses NVIDIA's CUDA to accelerate encoding, but has a higher CPU utilization than Badaboom. One review reported visual problems with iPod and WMV playback using Catalyst version 8.12, and although concluding there was no clear winner, if forced to choose would go with the Avivo converter.

A Guy

I'm not sure if it's appropriate to bump this old post but I'm looking for the same thing. I've already installed that package but I cannot see a video converter, instead, I see a checkbox that tells me that I can enable an option to automatically convert videos when copied to a portable device.

Is there any way to use this converter without the need to copy it to a portable device? Also, is there any other software that uses the GPU's power to convert videos?

Run Catalyst Install Manager and Uninstall AVIVO.
Then install the AVIVO Codec Package,
Then install the 11.1a Hotfix and AVIVO and the Transcoder should be installed into CCC2
under Video -> AMD Video Converter.

I just did it earlier today because I didn't have the Video converter in CCC2 after updating to 11.1.

Well, surprisingly, it now works. I went to the Catalyst Control Center to try and open the Install Manager to follow what you instructed and to my surprise it's there. I guess it was installed when I found the package about a week ago but didn't restart. I will report this now as solved. :)