If the customer sends you an original design or logo, they own the design.
If they send you the design in a format that needs to be cleaned up, and you do, then you own the use of the digital files for their purposes. But their artwork is theirs. It's probably theirs if they instructed AI to design it...And this is probably going to become a new area of law. So I just go on the principle that they own the design if they send it to me. I ask. If my Spidey sense says maybe they don't really own it, but who knows, I just have them put it in writing that they own it.
Then the fun starts...For example, the customer sends you a low resolution photograph of their logo (happens all the time). And you use your skills - or a subcontractor's skills - to make it a sharp eps file but don't sell the eps file back to them. Then you own that eps file to print their
signs, shirts, wall art, etc. Later, they come to you and say, we've got a new printer that's not you. Can you send us the file? You own that eps file. And when they ask, I say no. (Unless they are good customers and I think they just want a different format - like shirts that we don't do. And sometimes I get fooled for being trustworthy). They came to me in the first place with rough artwork because the abandoned their last printer. So the cycle continues.
I'm fair and give the customer the opportunity to buy the eps/high resolution file for a reasonable amount when doing the initial work. (They do pay for it, but pay more if they want to keep it.) And an unreasonable amount when they want to take the work somewhere else.