July 16, 2026

VIA EDGAR

Division of Investment Management

U.S. Securities and Exchange Commission

100 F Street, NE

Washington, DC 20549

Ladies and Gentleman:

Third Point Private Capital Income Fund (the "Fund") hereby respectfully requests the withdrawal, effective immediately, of the Fund's Registration Statement on Form 10-12G, filed with the Securities and Exchange Commission (the "Commission") on May 18, 2026 (Accession No. 0001104659-26-063294), together with all exhibits thereto (collectively, the "Registration Statement").

The Fund believes that withdrawal of the Registration Statement is consistent with the public interest and the protection of investors. The Fund is withdrawing the Registration Statement to prevent it from automatically becoming effective sixty days after the filing of the Registration Statement pursuant to Section 12(g)(1) of the Securities Exchange Act of 1934, as amended.

The Fund will refile the Registration Statement concurrently with the filing of this request in order to reset the statutory sixty-day effectiveness date.

It is our understanding that this application for withdrawal of the Registration Statement will be deemed granted as of the date that it is filed with the Commission.

Should you have any questions regarding the foregoing, please contact John J. Mahon of Cleary Gottlieb Steen & Hamilton LLP, counsel to the Fund, at (202) 974-1926.