Just a note - when using the REST API or VNMsh, you need to create the relation on every landscape that contains a member of the Global Collection. e.g. if you have 10 devices you want in the GC spread out on 3 of 10 landscapes, you will need to create a global collection model on the 3 landscapes and then create the device models (by adding the devices if not already there) then you need to create the relation for each of the devices.
E.g.:
Create GC (POST):
http://<OC_IP>:<PORT>/spectrum/restful/model?landscapeid=0x100000&mtypeid=0x10474&attr=0x1006e&val=<GC_Name>
Associate GC:
http://<OC_IP>:<PORT>/spectrum/restful/associations/relation/0x1003b/leftmodel/<Model Handle of GC>/rightmodel/<Device Model Handle>
Note: This is a static global collection - ie. you copy the devices into the global collection and the GC never changes.
If you wanted to create a dynamic global collection (uses some sort of logic to populate the GC) - you would need to modify the dynamicCriteriaXML attribute (0x12a6a).