Property partnerships end for a variety of reasons. Ideally, the ending is wanted and agreed upon, financially and emotionally enriching all parties. But when things go bad, stuff hits the fan. Likely circumstances are a broken relationship, a property investing business partnership that went south or siblings who shared property their parents left as part of an estate. A fourth category occurs when one partner in an amicable relationship wants to cash out and the other wants to keep the property and they don't agree on the property's value.
As The Orange County (CA) Register explains in "Splitting up property is hard to do," being level-headed, open-minded, and empathetic can really improve your odds of avoiding protracted litigation to force a sale of the property. The process is termed a partition action. If you are really interested in getting to a fair property value for all concerned, there's a formula for the situation where one party wants to purchase the other party's share and keep the property. In that case, each party chooses one appraiser, and each conducts his or her own appraisals. Then the two appraisers agree on a third appraiser to do another appraisal. The final value is an average of the two appraised values closest to each other.
Here's an example of how this works. Partner A's appraiser determines that the value is $650,000, and Partner B's appraiser values the property at $745,000. Then, the mutually-chosen appraiser conducts her appraisal and determines that the value is $690,000. The closest value to the third appraiser's estimate is by Partner A's appraiser: $650,000. The average of the two is $670,000. Party B's appraisal is thrown out. This type of methodology makes both appraisers reasonable so that their value isn't the one that's knocked out. A qualified estate planning attorney can help shepherd this process and refer you to appraisers as needed.
Reference: Orange County (CA) Register (November 7, 2015) "Splitting up property is hard to do"