Rumer Willis, Scout Willis, Tallulah Willis

Marion Curtis/

Demi Moore's daughters are managing to keep a low profile despite the intense media scrutiny surrounding their mother's health.

After Moore was rushed to a Los Angeles-area hospital on Monday to be treated for what her rep insists is "exhaustion," speculation erupted over who was looking after the trio.

Well, E! News can confirm that all three of Moore's children with ex-hubby Bruce Willis are doing just fine.

In fact, only the youngest in the clan, 17-year-old Tallulah, lives at the actress' Beverly Hills pad. Since her mom's emergency hospitalization, Tallulah has been staying at her dad's West L.A. condo.

"She's doing great," a family source tells E! News of Tallulah. "Her grandmother [Bruce's mom] is also there with her."

Meanwhile, Rumer, 23, has her own place in Los Angeles and visited her mom's bedside twice before Demi was discharged earlier this week. She was snapped by photographers appearing distraught while smoking a cigarette outside the hospital.

Scout, 20, is currently attending college at Brown University and hasn't been back in L.A. since the hospitalization, which came two months after Demi announced her decision to divorce husband Ashton Kutcher after he allegedly cheated on her.

The newly single Two and a Half Men star was in São Paulo, Brazil, this week attending the city's fashion week and modeling Colcci's new catalog when he learned about his ex's medical crisis. He declined to discuss the situation with awaiting paparazzi when he arrived back in L.A. last night around 8 p.m.

As for Willis, he has yet to comment on his ex's health scare, though E! News can confirm he was spotted driving around Hollywood yesterday.

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