It looks like you have two different grasses going on. The broader-leaved grass does look like Cortaderia, but the thinner-bladded grass, which seems to be blooming, is not.

How weird! I'm happy I do have the one I wanted though. I wonder should I leave it like that or try to separate them? Can anyone tell me the second grass' name? Looks like I got one strange bargain :)

Thank you for your help!

The awls on the other grass look familiar, but I'm not sure. Can you describe the stems which the flowering heads are on? I'm particularly interested in their shape...round, square, flat, etc..

The stems that hold the heads are round (tube) and the leaves are flat and V shaped. I'm not sure the correct terms but it has one long vein down the middle of the flat leaf. Best picture I could take. Thanks, you've been a really big help!