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Kate Hudson's arms avoided getting burned thanks to nature's sunblock, but her ass wasn't as fortunate.

Kate's vacationing in Ibiza but took a boat Thursday to the neighboring island of Formentera. The place is known for its muddy beaches and she applied liberally.

Martin Shkreli -- the controversial pharma exec people love to hate -- might have to part ways with some rare and historic treasures ... like an Isaac Newton manuscript!

New York state's tax board is going after Shkreli's insane collection of artifacts to pay down the more than $2.8 million he owes in back taxes.

The collection, kept in Shkreli's office, is nuts -- it includes a signed Charles Darwin letter, and an antique Enigma machine -- notably used by Nazi Germany to encode military communications. Also on the table:

-- Stacked, 2003 photograph of Jeff Koons

-- Original lithographs by Joan Miro

-- Signed letters from Augusta Ada Countess of Lovelace

-- Original Glass & Collage Chessboard sculpture by Dustin Yellin

-- 6 pills by Damien Hirst

The judge hasn't signed off on the order for Shkreli or his company to turn over the items. The infamous one-of-a-kind Wu-Tang album he purchased is not on the hit list.

Not yet, anyway.

The scores of celebs who met Wednesday night to figure out solutions to the racial divide in America were not in full agreement ... so says The Game, who was front and center.

Game and the others met at Cedric the Entertainer's home in the San Fernando Valley, and the rapper told us on "TMZ Live" there was some conflict over the mantra ... Black Lives Matter vs. All Lives Matter.

Game says in the end the group unified, and they'll meet again soon ... to start mapping out concrete solutions.

Dana White confirms to TMZ Sports ... he WILL be speaking at the Republican National Convention next week to talk about his relationship with Donald Trump.

The UFC honcho has been very vocal about his support for Trump -- and previously appeared on the "TMZ Sports" TV show on FS1 and explained why he's got Donald's back no matter what.

As for White's RNC speech -- Dana says it won't be political ... but rather, "It will be about my relationship with Trump and the Trump that I know."

Joshua Allen -- the season 4 winner of "So You Think You Can Dance" -- faces serious time behind bars after allegedly attacking his girlfriend twice in a 2-month span.

According to the D.A.'s Office ... Allen went after his girlfriend last month, chasing her inside a coffee shop when she tried to run away. When a woman tried to step in, Allen allegedly threw a glass vase at her and vandalized the shop before bystanders took him down.

He also strangled her in April, according to the D.A. At the time, she already had a criminal protective order against Allen for a prior domestic violence conviction.

Allen's been charged with 2 felony counts of willfully injuring his girlfriend, 1 felony assault with a deadly weapon ... and 4 misdemeanors related to battery, vandalism and violating the protective order.

If convicted ... he faces more than 10 years in prison.

It's been 5 years since her acquittal, and Casey Anthony's showing her loving, caring side again.

Casey's Yorkshire Terrier looked none the worse for wear after she picked it up from the groomer near her home in West Palm Beach.

Last Tuesday marked the anniversary of the day a jury found her not guilty of murdering her 2-year-old daughter, Caylee.

LeBron James issued a VERY SERIOUS warning to his ESPY after-party guests Wednesday night -- either you dance or "get the f*** up out of here!!!"

FYI, this video is awesome!

Bron took the stage at the Uninterrupted party at Le Jardin -- and made it clear he had no patience for the bougie Hollywood people who are too uptight to turn up.

"If you not dancing, shaking your ass or having a good time ... there's an exit sign right there!"

"So if ya'll not dancing having a good time shaking your ass ... ya'll got to go man."

By the way, the party was INSANE -- with a performance by Kendrick Lamar ... and SO MUCH DELICIOUS FOOD!!!!

Seriously ... check out this clip of DJ K-Love with his to-go plate -- "It's like mini-Thanksgiving dinner in that motherf****r right now!"

Kourtney Kardashian poured her little heart out -- into shot glasses -- during a random pit stop in Massachusetts.

Kourtney turned up Wednesday night at local dive bar The Chicken Box on Nantucket Island, and took matters into her own hands ... pouring Don Julio shots!

She did plenty of damage in her half hour visit ... jumping onstage with funk band The Soul Rebels and shooting a little pool.

MILFs still get down.

"Love & Hip Hop: Atlanta" star Stevie J says Joseline Hernandez is out to ruin his character, and calls her allegations he molested his 6-year-old daughter ... a sick attempt at revenge.

Joseline posted a message to Twitter earlier this month, claiming Stevie had molested the daughter he shares with Mimi Faust for years.

Stevie remained quiet about the claim until Wednesday when he filed for, and was granted, a temporary restraining order against Hernandez. In the docs, obtained by TMZ, Stevie calls Joseline volatile, jealous and says she's filled with an evil sense of revenge after their nasty split.

Kevin Hart's livin' large.

The superstar and fiancee, Eniko Parrish, are chillin' in Cancun ... a smart move on Kev's part after his all boys turn up last week in Vegas.

Cedric the Entertainer galvanized Black Hollywood Wednesday by hosting his own version of a town hall meeting at his L.A. home, and the guest list was stacked.

T.I., The Game, Beyonce's mom Tina Lawson, Jesse Williams, Tisha Campbell-Martin, Omar Epps, Meagan Good, Terrence J and Tasha Smith all showed up. We're told in all, around 300 people got an invite for the 3-hour get-together.

Prince Harry showed the world ... staying sexually safe and responsible is super easy.

Harry took an HIV/AIDS test in front of the cameras, to show the world -- and especially the thousands of people in the UK who have the virus but don't know it -- it's as easy as sitting down and getting results just minutes later.

The test is nothing more than a pin prick. In Harry's case ... he's negative.

Harry's making HIV/AIDS part of his royal agenda ... something his mom did as well.

Selena Gomez has a lead foot -- at least in reverse -- and a poor innocent fence paid the price.

'Bizarre Foods' host Andrew Zimmern has tried everything from raw pig testicles to bull penis soup ... but seriously, human flesh?

George Clooney just got legal protection from a mentally unstable guy who waged a war of harassment against the actor, his wife and others ... the question -- will it stop the guy?

Mark Bibbee sent 189 pages of rambling, delusional and disturbing documents to Clooney's team, among other things making veiled threats against the actor and Amal. Among the emails ... reference to an assassination plot against George H.W. Bush and the JonBenét Ramsey murder.

According to the docs, Bibbee has been diagnosed with bipolar disorder and possible schizophrenia.

There's a disturbing reference to the Orlando massacre, in which Bibbee writes, "Orlando is a false flag event to cover for LGBT criminal & pedophiles."

The judge ordered Bibbee to stay 100 yards away from Clooney, Amal and his team for 5 years and to cease all other contact.

Clooney and Amal are currently at their home in Italy and seem unfazed.

The 15-year-old girl voice of "Dora the Explorer" attempted to bully a classmate into smoking by calling her a p**** ... according to a lawsuit filed the classmate's parents.

The parents just filed new docs in the suit which include quotes from the anonymous student describing the encounter. She says Fatima Ptacek was encouraging her to smoke a vape pen. The girl says, “I told her I didn’t want to, but she called me a ‘p—y’ and my competitive side kicked in.”

In the docs, the girl adds Ptacek “said some very unkind, hurtful things that in the moment made me feel vulnerable.”

The girl's parents are pissed because after the incident their daughter was expelled from her $40,000/year Manhattan private school, while Ptacek merely got a 3 week suspension ... according to the NY Post.