Final answer:
The U.S. Supreme Court case that dealt with the competence of appointed attorneys was Betts v. Brady.
Step-by-step explanation:
The U.S. Supreme Court case that dealt with the competence of appointed attorneys was Betts v. Brady. In this case, the Court established the principle that the Constitution does not guarantee the right to appointed counsel in all criminal cases. However, it also recognized that in certain circumstances, the denial of counsel might violate the due process clause. The Court set forth a test to determine whether the circumstances of a particular case required the appointment of counsel.
Learn more about Competence of appointed attorneys