Are purchasers in a probate transaction required to submit a deposit of 10% of the purchase price in Los Angeles, Orange, Riverside, San Bernardino, or San Diego Counties?

The answer depends on whether your have full authority or limited authority:

Full Authority: 
If you are afforded full authority under IAEA there is no minimum deposit required when selling real property of the estate.  You basically would handle the sale like a non-probate transaction.  The only caveat is that a notice of proposed action must be sent to all estate beneficiaries so they can have the opportunity to review the terms of the sale and object or approve the sale.

Limited Authority:
If you have limited or no authority under IAEA then you must petition the court to approve the sale of real property.  There is no statute delineating a minimum deposit when selling real property.  However, it is customary-and advisable to require a deposit of typically 10%.  A 10% deposit seems to be the unspoken rule in sales of real property in Probate.  In reviewing the rules of court for L.A., O.C., Riverside, San Bernardino and San Diego, I found a rule pertaining to minimum deposits of 10% for San Bernardino and San Diego County.