It looks like AMD Tri core will be a desktop thing only. It will be branded as Phenom X3 and it is expected in early 2008.
The codeneme of the CPU is Toliman and the chip comes in AM2+ and supports Hypertransport 3. It looks like it will be made of the fallen Quad core K10 cores but I guess that Amd will try to make a demand of these parts.
Toliman should not be much more expensive than Kuma, dual core K10 and both chip have 512KB cache per core and 2MB L2.
Availability is scheduled for Q1 for both Toliman and Kuma.