If I have paid for a small piece of a larger property, and money was exchanged for said piece of a building, can the majority owner mortgage off the property without my consent?
The real answer, as with most legal questions, is “it depends.” But I’m going to go out on a limb and say probably yes. If your co-owner can find a lender who’s willing to do so, he can get a mortgage that’s secured only by his interest in the property. More commonly, lenders will insist that all of the owners sign off on the security interest (even where they aren’t personally responsible for the loan).
Also, depending on the agreement between the parties, the majority owner may have reserved the right to borrow money using the property as security. You would need to review all the purchase documents to see if this is the case. The majority owner can’t burden your portion of the property without your consent, but make sure you haven’t given that consent already.