All applications to Duke and UNC-Chapel Hill are theoretically considered for the Robertson, but it's strongly recommended that you fill out the supplemental materials form because that's the only way to ensure that the Robertson staff directly review your file.
39,000 people each year apply to UNC and/or Duke each year, so filling out the form is probably a really good idea. It is due December 1.
For those unfamiliar with the program, here's a basic rundown:
The Robertson Scholars Program is a full-ride merit scholarship and leadership development program at Duke and UNC-Chapel Hill that covers all college costs (tuition, fees, room and board, laptop, books, etc.). It also provides full funding for three summers of global travel, research, and internships, and gives recipients a unique “dual citizenship” where they are full students at both Duke University and UNC-Chapel Hill.
Selection criteria: The Robertson program seeks out students who will be change agents, innovative leaders who have the potential to have a profoundly positive impact on the world. Criteria for selection include superior academic achievement, intellectual curiosity, strength of character, courage, and collaborative spirit.
More info:
Robertson Scholars: Homepage 
