To own the copyright in it? Blockchain doesn't really do much here because ownership of copyrights is determined by the legal system not by a blockchain. (And normally when an artist sells an artwork they keep the copyright themselves; you only get the copyright too if you specifically negotiate with the artist for that, or if you commission the art as a "work-for-hire".)
To own the only digital copy of it? Blockchain does nothing to stop people making more digital copies of it. Blockchain is not a DRM system.
It seems like "owning" digital art where one doesn't have the copyright or exclusive possession of digital copies is basically a meaningless form of ownership. It is the status of "ownership" stripped of all substantive content.
Full rights can be attached to the artwork, as was done with the Hashmasks sale: https://www.thehashmasks.com/
It is completely up to the artist to customize. It can be embedded into an NFT just like a license.md file can be embedded into an open source code repository. It can be explicit, rights can be transferable, or non-transferable.
Any other address producing an NFT is a forgery.
Blockchain is better than a DRM system. See:
https://audius.org/developers https://opensea.io/blog/announcements/opensea-raises-2-milli... https://eulerbeats.com/
You can't copy a Bitcoin. And you can't copy an NFT.