As the world watched her win the Best Actress Oscar for "The Hours" last month, Nicole Kidman paid tribute to her mother and 10-year-old daughter, Isabella, in the Kodak Theatre audience. But she also shared the night's victory with her ex-husband, Tom Cruise, and their 8-year-old son Connor, reports PEOPLE.

On Oscar night, the magazine reports in its latest cover story, she rang her ex on her cell phone as he was on the set of his "The Last Samurai" in New Zealand.

"It was so important for me to talk to Connor and, yes, to Tom," Kidman, 35, says. "We have very different lives now, but as I've said to Tom, I will be there for him for the rest of his life, always there."

As she explains, "There's a beautiful moment in 'The Hours' when (Woolf says), 'Always the years together, always the hours,' and Tom and I had 11 years together. Your heart has to stay loving. For the kids, it has to be."

Cruise, 40, offered congratulations; Connor, who'd been practicing push-ups during the awards, "was happy for me but slightly disinterested," Kidman says with a laugh. "But he knows that if Mommy or Daddy ever gets nominated again, then he gets to go."

In the interview, Kidman now refers to herself "very single" and she denies tabloid newspaper rumors about a romance with British actor Jude Law, her co-star in the upcoming "Cold Mountain."

"He's a wonderful man and a good friend of mine, but there was no affair. We spent seven months shooting and it's an intense love story so we were waiting for that. They did it with Ewan McGregor, too, on 'Moulin Rouge'," she says.

As for the sort of man she's ready to welcome into her life: "I want someone who says, 'I will stand by you and be there for you and your life is just as important to me as mine ... I'm waiting for someone to come rock my world."