I have seen an anime in which monsters come in the human world. I think there are cards which are used for summoning monsters. They are also divided in one star, two stars, three stars, four stars. Also there are two different monsters which fuse and become a new more powerful monster. That goes on until the monster becomes the ultimate monster. And also there was a monster with a main character who was an ultimate monster and transformed in its actual shape which combined with other 8 or 10 ultimate monsters at last.
It's not cardfight, vanguard or yu-gi-oh.