Garrett style center cartridges fit deep into the register of the turbine housing. Chances are if the turbo has a lot of miles on it, then it's probably coked in there good and tight because of the heating and cooling the turbo experiences while running. Olson has the right idea, heating the area where the turbine housing and center cartridge meet, and using a mallet, or in severe cases, a a ball peen hammer is the best way to get it apart. Just be sure it doesn't come out cocked, and damages the turbine wheel.
Garrett CHRA's don't use a alignment dowel like MHI TDO5 turbos do. They rely on the lockplates and bolts to maintain the position of the CHRA, compressor cover and turbine housing relative to each other.
In the shop I used to work at, the way I was taught to deal with a stubborn turbo that didn't want to come apart, was to secure the turbo in a bench vise with the compressor housing pointed up. Make sure its in there tight, because chances are you're gonna wind up beating on it a bit.
We used a penetrating fluid called KROIL to soak the bolts, and the register of the turbine housing. After allowing it to soak a bit, we'd start by removing the bolts and lock plates, then try to tap upwards on the back side of the compressor cover with a mallet. If that didn't work, we'd go with a larger ball peen hammer. I wouldn't hit the backplate of the compressor cover directly, but rather the heads of the bolts securing the lock plates to the compressor cover. If they get dinged up, it's no big deal to replace them. This method worked about 75% of the time. The other 25% required a torch.
We had a Oxy/Acetylene torch that we used for this. If it was being a bitch, we'd heat the register of the turbine housing as evenly as possible to try and get it to expand a bit. Ball bearing center cartridges were tricky, because the bearing cages were made of plastic, so as soon as the CHRA was freed, we'd take it to the parts washer and run some solvent through the water feed lines to cool the bearing housing. Journal bearing turbos are a bit tougher, to hurt.
The heat would usually do the trick, but every once in awhile you'd have to get froggy with one that was being extra bitchy. Like, mashed, deformed compresssor clamp bolt heads, froggy. Good thing we had plenty of those bolts on hand to replace ones that got damaged during the teardown.
Be sure to wear gloves, as I found out a few times that the turbine housings tend to retain heat for awhile, even after they look like they've cooled down. /ubbthreads/images/graemlins/grin.gif Oh and if the turbine housing is extra crusty and corroded be prepared for snapped bolts, or rounded off fastener heads. I got pretty good at removing rounded off fasteners with a hammer, a brass drift and occasionally, a chisel.