Welcome to our forum.
"I'm not interested in having a relationship with someone who goes off to have a seperate relationship with someone else."
Do you mean that you wouldn't want any of your partners to have other partners at all, or just that you would want everyone connected to the group to be close to one another (or even living together)?
"I don't know if that is polyamory, but I saw the show on Showtime and it really struck a cord with me."
If it involves romantic/consensual ties between more than two people, it's polyamory. (At least that's my definition of it.)
It sounds like you aren't the type to be rushed, and would do well to ease into things, getting to know people a little at a time. I would recommend doing much reading/posting on these boards and getting very familiar with the ins and outs of polyamory, as well as getting to know various polyamorous people.
I hope we're able to help.