Where should a community live?

During a great discussion with a knowledgeable client on communities we discussed "Where should a community live?". This seemed like such a simple question when there was the "Social Media Land-grab" they live on our site. But now we have a handful of main community infrastructures. Facebook, Twitter, Linkedin and MySpace (others in other languages) it is a little more in-depth.

It seems dated to expect your community to only talk in your environment, the community will talk where they want and where they feel comfortable. This means that as communities grow we will either on have a few environments or the tools will grow (Open Social, et al).

The question was asked, "Does a community need to live anywhere.?" The community as long as it's members can be identified can live in many different / parallel environments.

Do you agree?