On 99designs, designers agree to upload only original artwork, so each designer owns the rights to their design submissions.
This is true until the client chooses one of the designs as the contest’s winner. Then, and only then, can the designer agree to transfer his or her rights to that particular design to the client.
The designer transfers their rights in the Design Handover stage, and once it’s done, the client becomes owner of the rights to that design.
If a designer creates several design concepts for one contest, but the client only buys one of them, then all the unused design concepts remain the property of the designer. The client can, of course, negotiate with the designer for the transfer of rights to more than one of their designs.
If the client does not buy a designer’s work, it remains the property of the designer.