Can I copyright something on behalf of another person?

I’m afraid the Copyright Act beat you to it. Copyright arises automatically under the law at the time a copyrightable work is created and “fixed in a tangible medium of expression” (e.g., drawn on paper, saved in digital format, recorded on tape, etc.). What that means is that your cousin’s logo design was protected by copyright law as soon as she created it, and she has owned the copyright since that time.

What you may be thinking of is the act of registering a copyright with the Copyright Office. Registering a copyright doesn't create the copyright itself — it simply records a person’s claim to a particular copyright with the federal government. (It also provides some very valuable benefits in the event someone infringes the copyright, which is the primary reason most people and businesses do it.) Unfortunately though, you aren't permitted to register someone else's copyright unless you’re acting as the copyright owner’s authorized agent. So, at least assuming you want the gift to be a surprise, the Copyright Office won't permit you to register the copyright in the logo since you don't have your cousin’s authorization. But you certainly can help your cousin do it herself or even ask her for authorization to be her agent for the purpose of registering the copyright.

                                                                                                                                                               

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