Zynga apparently started promoting its new pet-caring game, PetVille, on Sunday, just a few days after launching it. Now, the game has nearly 6 million users.

This is not the first time that Zynga has had a social game become this big, this fast — it saw similar results with its two most recent releases, Café World and then FishVille. Its tactics typically include featuring the newest Zynga game on the toolbar it runs across all its games (meaning access to tens of millions of its usrs), as well as buying Facebook advertising. As we noted earlier this week, PetVille has gotten prime real estate on the toolbar.

But if anything, the huge growth in just a few days suggests the company is putting extra effort into making this one big. While the game actually went online on the third, promotion didn’t kick in until Sunday, judging by the numbers.

Interestingly, PetVille comes shortly a new potential rival to Zynga, CrowdStar emerged with a new pet-caring game, called Happy Pets. That company had a huge hit earlier this fall with Happy Aquarium, a virtual aquarium-caring game that has inspired a number of others, including FishVille. CrowdStar chairman Peter Relan recently told us this: “Every time they enter a category where we have gotten big, we’ll launch an entirely new game within weeks.” He told us to expect a new one this month.

Like many in the social gaming world, we believe that there’s room for many different developers to build a lot of popular games. But a lot of those games will likely continue to be made by Zyng.a