"They were intensely close, and Paul would do almost anything for John." (George Martin)
"It was an extremely deep relationship." (Ken Mansfield)
"It was deeper than any of us will ever know." (Linda)
"It was an intensely close relationship." (Tony Barrow)
"If Paul was a woman he would have been a great threat because there's something definitely very strong between John and Paul." (Yoko)
"They were closer than any two men I've ever known." (Alistair Taylor)
"Paul and John were so tight it was like one person at times." (Roger McGuinn)
"Paul and John were emotional partners in a powerful, creative and loving way." (Paul Saltzman)
"That Paul started painting after John's death is no coincidence. That competition, the clash, the ebb and flow of that relationship, was so central to Paul's being, the only love that comes close to being a reasonable comparison is his marriage to Linda and the births of his children." (Francie Schwartz)
"They were so intertwined and so tight on so many different levels." (Maggie McGivern)
"Paul and John were the best pals. They spent all their time together and stuff, and they had individual lives. But in the end they were the final sort of arbiters of everything between themselves." (John Dunbar)
"John and Paul clearly had the closest friendship in the Beatles." (Geoff Emerick)
"No deep relationship in the world is ever totally smooth, and ours was one of the deepest." (Paul)
"He's the closest friend I've ever had, except for Yoko." (John)
------------------------------------------
Note: This is an answer to some comments I've seen, saying that John and Paul weren't really that close (Philip Norman and other authors have even claimed that they just had a professional relationship).