The required application form is at the link http://doa.alaska.gov/dmv/forms/pdfs/809.pdf The form must be NOTARIZED.
In person. Bring the form to a DMV office. Locations can be found at http://doa.alaska.gov/dmv/office/index.htm
RELATED LINKS:
TITLE INSTRUCTIONS FOR SELLING A CAR IN ALASKA
REPLACEMENT TITLE – ALASKA
You cannot transfer ownership of your vehicle if you do not possess the Title Certificate. The most common reason you would not possess the Certificate is that there is a lienholder (lender) for the vehicle. In this case the lien holder maintains control of the title until the lien (loan) is paid off. This common situation does not require a replacement of the original title, but instead a transfer of the title to you.
REPLACEMENT. The title must be “replaced” if the original has been lost, damaged (rips, coffee stains, water damage), has cross outs or white outs, or has incorrect entries (such as seller’s printed name and signature not matching the official names on the front of the title) or signatures in the wrong place.