But how will the magazine's editors know whether or not the person was being harassed or hassled?
"If a judgment call has to be made, that's when we go to the representatives for the celebrity," Min said. "And for celebrities who have contacted us and asked us not to run their kids, we don't run the photos."
But Us Weekly recently featured a photo of actress Reese Witherspoon on vacation with her children, and actor Jake Gyllenhaal. Witherspoon and her children appear to be shielding their faces.
"Reese Witherspoon, Jake Gyllenhaal have a relationship that our readers are really interested in. The fact that they went away on a family vacation all together is definitely of interest to the audience," Min said. "My feeling on that is, there are many photographs of Reese Witherspoon and her children we do not run. I mean that one, I would definitely say is right on the line."
The constant presence of cameras is enough to infuriate even easygoing celebrities like Parker.
"I was walking my son to school and [kids are] just so chatty in the morning," she recalled. "And I love that time with my son. And when we are followed by photographers, which we are on a daily basis, they're just, I feel like they think they have to be there. Like they punch in or something. They're getting too close and I'm trying to block him and keep my head down. And these guys just, they're enjoying it. They're enjoying it. And I just, I just screamed.I just said, 'Leave me alone.'"
Parker said the photographers were "stunned" and walked away.
Confronting the photographers is something Hayek has tried as well, like during a stroll through New York's Central Park with her daughter and fiancé, captured on video by the paparazzi. "I saw these two French guys, and I was so angry and I said, listen, take your picture and get out and just leave us alone," she said. "And they said, 'OK.' And they left."
"See, if they were like that, I wouldn't have a problem. But that was because they had been following us for two hours and they already had hundreds of pictures."
Over the years, this kind of attention can take a toll on children, as Parker has seen with her son.
"It makes him not particularly inclined to take family photos because he has a relationship with the camera that's antagonistic," she said. "He hides. His class pictures for two years have been this [Parker covers her face]. And I think it's a shame for him."
But for all of those who hate the attention, Janice Min said there are plenty of stars who invite it.
"Children have played a great part in enhancing the connection between celebrities and their fans," said Min. "I think any parent who's entered into celebrity would have to consider that when they have children these days, that paparazzi will be part of your life, will be part of your children's lives."
"I don't think it's right that these people make money out of your private life," Hayek countered. "Who is deciding what's the price of fame? The baby did not choose to be a celebrity. And the parents were never participating in this decision."
"The paparazzi are the interlopers. We're not. We're not going anywhere," Parker said.
"You know I can cope with it," Hayek said. "Just don't mess with my children."