The Oath exists where the claim is one of theft, as well, although a thief is not believed in oaths: Bava Metzia 5a-b
Whether one swears that he owns half, or that he owns no less than half: Bava Metzia 5b
Admission and its Equivalents
Admission must be on the same type of object as that of the claim: Bava Metzia 5a
Existence of Witnesses on part of the sum are equivalent to the lender's admission on part of the sum: Bava Metzia 3a-4a, 5a-b
Cases
[Not] Requiring an oath if the defendant admits to owing less than a perutah: Bava Metzia 55a
[Not] Requiring an oath if the defendant says "Here they are, take them [Heylach]": Bava Metzia 4a-5a
Admitting that one wrote a Bill is equivalent to saying "Here, take them [Heylach]": Bava Metzia 4b
If one denies another's Claim on Territory, but admits to his claim on Vessels: Bava Metzia 4b-5a
If one denies another's Claim on Vessels, but admits to his claim on Territory: Bava Metzia 4b-5a
If one denies one type of vessels, and admits to another type of vessels: Bava Metzia 4b
If collateral is lost, and the lender says it had been worth half of the loan, and the borrower says it was worth 3/4, the borrower should swear as an Admitter of Partial Debt, but the Rabbis made the lender swear to prevent a scenario where he waits for the oath and then "finds" the object and disproves the borrower: Bava Metzia 34b, 34b-35a
If collateral is lost, and the lender says it had been worth 5/4 the value of the loan, and the borrower says it was worth 3/2 the value, the lender swears as an Admitter of Partial Debt: Bava Metzia 34b