If there was some kind of agreement in place, be it written, oral, or even implicit (unstarted, but obvious), then you can sue each other and ask a court to figure it out.
If no money has changed hands, then it would make it much harder to argue that any rights have changed hands either.
If the code in the git repo is already covered by some license, say MIT or GPL, then it could be argued that any contributions to the repo are automatically covered by the same license.
The author retains full copyright and ownership over their creations, but they've permitted others to use their work under the terms of that license.
If you have no agreement, no license, and no payments have been made, then the author is almost certainly still the only rights holder.
If there's multiple authors to the work (e.g. a Git repo of lots of code), then this is a huge murky grey area... which is why you want all the contributors to be agreeing to the same license conditions... or you want all contributors to be employees of the same company.
With no agreement, you have no rights to use their work. It could be argued that by submitting their work to your project, they were agreeing for you to have rights to use them... but do you really want to have to argue that through the legal system if needs be?
* If this is volunteer work: Get some contributors agreements made up, and make your contributors sign them... now.
* If this is paid contract work: Get some decent contracts made up.
** In either of those two cases, they can retain copyright on their work if you/they want, but they should grant you unlimited license (or similar) to their work.
* If this is for full-time work: You're probably covered by employment laws and are ok, but you probably want to ask your lawyer to be sure.
A complete and total transfer of copyright (where the author now has no rights, and you own their work completely) often only happens between an employer and their employees. In most other situations, the author retains copyright over their work for life, and they grant other people license to use it (either with certain conditions attached, or "unlimited license", which is almost the same as duplicating the copyright).
Edited by Hodgman, 22 June 2014 - 05:02 AM.