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Kim Kardashian and Kanye West aren't committed in matrimony ... but they ARE committed in 11 million (and one) other ways -- TMZ has learned the duo just bought an$11 MILLION MANSION!

Sources close to K & K tell TMZ ... the future parents are now the proud owners of a 10,000-square-foot pad in an über-private, gated community in Bel Air, CA.

Kim and Kanye have owned the house for a few weeks ... and they've already gutted it and are designing a 14,000-square-foot dream home in its place.

The new home will be an Italian-style villa  ... with a gym, movie theater, full hair and makeup salon, bowling alley, basketball court, indoor and outdoor pool ... oh and probably a baby nursery. Just a hunch.

Not included ... a wedding date.  We're told there are no plans.

FUN FACT: Kim & Kanye's new neighbors will include Jennifer Aniston, Chris Paul, and Joe Francis.