updated 06/22/2011 AT 6:45 AM ET
•originally published 06/21/2011 AT 9:00 PM ET
But Tuesday night, Hilton told TV host George Lopez on Lopez Tonight, “We’re not together anymore. I love him and we remain really good friends … I feel like the relationship ran its course and we’ll see what happens.”
Then came the statement from Hilton’s rep, Dawn Miller: “I can confirm that Paris Hilton and Cy Waits have ended their relationship. It was a joint and amicable decision. They both have respect and care for one another and ask for you to please respect their privacy.”
The couple’s relationship played out publicly on Hilton’s Oxygen series The World According To Paris. In a recent episode, the two were seen arguing.
“Paris still thinks of Cy as a great influence on her life,” a friend tells PEOPLE, “but she’s just not ready for the next step in a relationship.”
The friend adds, “they definitely are still friends.”
Hilton told PEOPLE about her reality show last month, “it’s like me going through the transition of turning 30, which has been really interesting. I feel like I’ve lived such a life and what else can really happen?”