Payment conditioned upon closing the loan does not in itself create a partnership relationship. In most states creation of  general or limited partnerships are usually governed by statute or common law.

It is possible to condition payment to an abstractor as a third party vendor upon closing the loan, but that would have to be the intent of the parties when the title search was ordered. In the absence of the written agreement...the terms and conditions on the order become evidence of the oral agreement. If there is no conditional payment mentioned...it is going to be difficult for the defendant to assert the condition as a defense. No abstractor should accept an order unless his fee is referenced therein.