Is this the case for links in all user-contributed content? Or are links nofollow only for new users (or users with less than some amount of rep or time on the site)? Are links within the site (for example, to another post here) nofollow, or just those linking elsewhere?
The links in content generated by users are by default nofollow. This, however, changes once the post exceeds a predetermined vote and age threshold. The exact number of votes and the age has not been made public for concerns of gaming the feature. I am not sure if there are any distinctions between an external link and a link to another post in the same site. See Remove nofollow on links deemed reputable.
I am also of the opinion that when the post gets edited, the age threshold is reset again to ensure spam link doesn't get edited in. The details are pretty much fuzzy for obvious reasons.
On that note, the website column in any user's profile is nofollowed until the user hits 2000 rep. However, no links in the About box are followed. This is true irrespective of the rep of the user.