Ashton Kutcher has not abandoned his surrogate family when his marriage to Demi Moore fell apart, because we got video of the actor front and center at a Rumer Willis concert in Hollywood -- and who knew she could sing?

Rumer performed at The Sayers Club last night, and she's pretty good. One of the songs she performed -- "High Low Middle" -- something that is probably a metaphor for her life in the last few months.

Although you don't see Ashton inside the club while Rumer is singing, we're told he was on his feet cheering her on. 

Rumer Willis' Hollywood Hills home has been burglarized ... and the thieves made off with roughly $10,000 in stolen goods -- TMZ has learned.

Law enforcement sources tell TMZ ... Rumer's house is under construction and currently unoccupied.  So far all cops know is that in the last 24 hours, someone entered through an outside gate ... slicing through a lock with a blow torch type device.

According to sources, the burglar entered the home and snatched up roughly $10,000 of the contractor's tools ... before taking off.

It's unclear if any of Rumer's personal belongings were also taken.

We're told the incident is currently under investigation -- so far, no arrests have been made.

Rumer Willis knows if her mother Demi Moore has entered a rehab center for substance abuse ... and Saturday night she MAY have revealed the truth on camera.

Rumer was arriving to Comme Ca restaurant in West Hollywood ... when a paparazzo asked her, "Is Demi in rehab?"

It sounds like Rumer says, "No" ... but her purse was over her face, so it's hard to tell if Rumer said the word ... or if it came from another woman in the area.

Check out the video ... decide for yourself.

Rumer Willis returned to the Hollywood party scene last night ... slinking into a SAG Awards after-party just 6 days after her mother partied her way into the hospital last week.

Rumer -- who was at her mom's home when Demi went into a semi-conscious, convulsive state last Monday -- was seen entering the legendary Chateau Marmont hotel on the Sunset Strip last night ... by herself.

As we previously reported, Rumer and Demi had been partying together in Hollywood just 2 weeks before Demi's medical emergency.

We're told Demi is still receiving treatment for substance abuse.

Party All the Time

Rumer Willis was at her mom's home when Demi Moore went into a semi-conscious, convulsive state.

If you listen to the 911 tape -- around the 00:54 mark -- you'll hear the caller ask, "What is the address Ru?"

What's interesting ... Demi was clearly smoking something and, we're told, inhaling nitrous oxide with her daughter right there.

Rumer, who is 23, was partying with Demi just 2 weeks ago in Hollywood.

Rumer Willis paced and smoked a cigarette outside the hospital where her mom, Demi Moore, was taken for substance abuse treatment.

Rumer was visibly distraught and concerned Tuesday afternoon ... as she spoke on the phone. Rumer and a nearby friend had hospital visitor's passes on their jackets.

TMZ broke the story ... Demi was rushed to the LA area hospital on Monday night. Demi's people say she is staying at the hospital to seek "further professional assistance" to treat exhaustion and deal with substance abuse issues.

Zac Efron was drinking with good friend Ryan Rottman literally minutes before Rottman was arrested for DUI.  The question, should Zac have said anything to his pal to prevent him from taking the wheel?



Sources inside the Dillon's Irish Pub in Hollywood tell TMZ ... Zac, Ryan, Rumer Willis and a few other friends ordered a total of  7 Kamikaze shots, 8 or 9 mixed drinks and 3 - 4 beers.

Zac and Rottman both left the bar at around 9:30 and went their separate ways.  We shot video of Zac running from the bar to his car, though it appears Rumer drove him away. By 9:45, Rottman was in police custody.



Rottman apparently was hammered.  Cops spotted him after he drove up a curb near Dillion's.  He blew a .19, more than twice the legal limit.

We asked Zac's rep if the actor urged his friend to take a taxi or find some other way home that would not have put him behind the wheel.  We did not get a response.

So we ask ...

Former "American Idol" Kellie Pickler and celebuspawns Kelly Osbourne and Rumer Willis sat quietly  next to each other at a fashion show in NYC on Tuesday.


Question is ...
 

"Gossip Girl" sometime star Michelle Trachtenberg, 24, and Demi Moore's daughter Rumer Willis, 21, both showed up to the same event in NYC on Tuesday.


Question is ...

Here's Scottish actor Alan Cumming (left) in a production of "The Bacchae" at Lincoln Center on Wednesday -- and Bruce Willis and Demi Moore's 19-year-old celebuspawn Rumer Wills (right).

One of them is in costume.

We're just sayin'!

So you've got Seth Rogen, Jonah Hill and Paul Rudd -- three of the, arguably, funniest guys out there right now -- why the hell ask them about Ashlee Simpson & Pete Wentz's engagement?!

Also in L.A.: Mila Kunis, Kristen Bell and McLovin' all blew off fans outside the Kodak Theater, Rumer Willis had her very own pap crush, Kevin Richardson was mistaken for another Backstreet Boy and Kim Kardashian got a public berating by her own sister.

In NY: Michelle Trachtenberg dodged questions about rumored BF Chace Crawford, Kiefer Sutherland went out with his new chick, and Ben Stiller struggled to remember the name of Derek Zoolander's infamous pose.