Papillary thyroid cancer or papillary thyroid carcinoma is the most common type of thyroid cancer, representing 75 percent to 85 percent of all thyroid cancer cases.It occurs more frequently in women and presents in the 20–55 year age group.rom Wikipedia, the free encyclopedia. Papillary thyroid cancer or papillary thyroid carcinoma is the most common type of thyroid cancer, representing 75 percent to 85 percent of all thyroid cancer cases. It occurs more frequently in women and presents in the 20–55 year age group.