A partition sale divides up the property (if that's possible) or orders the sale of the property and divides the cash. That's done based on each owner's respective interest in the property. Thus, as quincy says, you won't lose your percent interest in the property if it is sold in a partition sale. The problem is that in court ordered sales the winning bids are typically significantly less than the market value of the home. If it's going to end up being sold in a partition the owners would do better to put whatever dispute they have aside and have a regular sale of the property and divide the cash. There will be more cash to go around that way.
Pardon me for calling attention to the inaccuracy of your response. It is not entirely in conformity with California law and hence misleading.
It is true that property sold via an action of partition can be ordered sold to the highest bidder at a public auction. However, in Californian (unlike some states) when it appears to the court
that a private sale will be more beneficial to the parties the court has the option of directing the referee to dispose of it (or part of it) by private sale.
The real problem rests with the excessive costs of such a procedure (referee's fees, attorney fees, appraisal fees, etc.,) all of which must be borne proportionately by the respective and often hapless co-owners. Consequently, the act of compelling sale by court order should be the last resort. And perhaps with so many vested owners it was the only option. Often it is difficult get two owners to agree on selling termsand here we have several.
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Section 873.520 California Code of Civil Procedure - Part 2 of Civil Actions - Title 10.5 Partition of Real and Personal Property