I Do Not Own/Headscratchers

I wonder if "I do not own" has a legal weight if that's my work licensed under copyzero license?
- The license does, these words don't. Basically, by default, as the copyright holder, you can do anything with your work and others can do nothing. To release your rights explicitly, put the work in the public domain (but be warned that not all legislations have the concept of public domain) or use a public-domain-equivalent license.

The ever-so-popular "All copyright goes to the original owners!" If you made it, you should know who owns it.
- Slightly less common is a Did Not Keep The Research version, in which the video maker used Fan Art (example) but never wrote down who made what as they went along, and asks viewers to help them find all the pictures.
- I make a ROM hack of Zero Wing. With Toaplan defunct, who bought up its copyrights at auction?
- This particular variant is actually used in professional works on occasion, such as video games (they'll typically have the copyright notice for each and every library or tool in the full credits, but everywhere else it's abbreviated). Besides, if the whole "placating acknowledgment that you have a copyright and then making this anyway" thing is a farce to begin with, does it matter?