(Disclaimer: I am not a laywer.)
If you don't have a contract, then you're SOL. You gave away your intellectual property without any restrictions on its usage.
You did own the copyright until you handed it over to the other person. You deliberately made the artwork to be used as corporate identification, not just a one-off T-shirt or poster, so your original intent was clear. If the other person has been using the artwork for any length of time, and has built up any kind of visual equity, you've lost any claim you might have had.
If you didn't get paid, you're also SOL. Not that you might not deserve monetary compensation, but at the time you did not ask for or expect any (underscored by the lack of contract), and if you were in a relationship, the "payment" might have been in affections.
Consider it a lesson learned. Don't do anything without a contract, even for friends/partners/family.