I'm glad that Adrianne specified what she was asking, but several people in THIS thread still have those unfortunate misconceptions I mentioned above.
The OP and relevant replies have largely expressed concern with typical or potentially worrisome arrangements they have personally seen tacked onto co-ownerships because reality is that most co-ownership arrangements go beyond merely a name on paper and involve other expectations and responsibilities. It behooves one considering such an arrangement to know what is normal, what to look for, previously exploited loopholes, etc. Yours apparently don't. Fine. Others do. They are not all the same...hence the thread. It's really not a difficult concept.