I'm Lucy, and I'd be happy to answer your questions today.
A third party can never make you sell the property at below market price. If your ex did transfer his share to a third party, and they tried to force a sale, the judge would allow you to have the property appraised and get a realtor who could work toward getting a fair price for the property. If you're concerned because you'd only be willing to sell at above market value, that could be a problem. However, in that scenario, you could ask the judge to order the third party to sell their share to you for whatever price they're trying to sell the house for (at which point, you'd be the sole owner and could later sale at any price where you found a buyer.).
Also, most reasonable people don't want to buy a lawsuit. Most people don't want to own half a house with a stranger. So it would be unusual to find someone who was willing to take half the house and then go to court to force a sale, because that would be really time consuming and expensive for this hypothetical third party. Someone would have to be a good friend or a relative of your ex to even consider it. And if you have evidence that your ex intentionally transferred his share to a third party in order to force you to sell, you could ask a judge to undo the transfer as fraudulent and hold him in contempt of court.
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