Not a lawyer, but pretty sure gifting and selling art does not transfer any of your rights as the artist whatsoever to the receiver or purchaser. Obviously they have the right to sell or give it away to someone else, but still, there is no transfer of rights to that secondary person.
The only time rights would be an issue is when you do art for a client. And even then, you still retain the rights to the artwork itself, while giving the client the rights to reproduce it in whatever way was agreed upon at the initiation of the project.
Doing art as an employee of a company is another issue, usually stating that any work you do while employed by said company, belongs to the company.
Probably more than you wanted, but hope that helps.