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1.
A relationship based on strictly just cuddling. This person may be known as your cuddle buddy.
"I am jealous of Brittany's cuddleship."

"I am too. I need a cuddle buddy. I want a cuddleship!"
by Sam's Theory September 26, 2011
 
2.
That point when it's excelled past friendship to the point where you can platonicly cuddle
"Are you guys dating?"
"Nah were just in a cuddleship"
by KittyKatty February 11, 2014