Root words: Fu, meaning Fuck, and Lationship, meaning Relationship.
A Fulationship is having a false relationship with someone based only on having sex.
Unlike Fuck Buddies, which are friends who have sex with eachother... In a Fulationship you don't even have to like the person, your only in it for the sex.
"John is in a Fulationship with Jane... He doesn't even like her!"
"I think i want a Fulationship with Jane because she's so hot, but man is she stupid!"