The article presents a scientometric analysis of the development of the carbon nanotechnology (NT) direction for 2000-2015 with the participation of 30 most active countries. It shows shifting the world research center to the Asian region, both on volume and quality indicators. Using the concept of a national research portfolio gives deep characteristics of different countries behavior in the course of scientific rivalry. Due to the strong skewness of the citation distributions, preference is given to the percentile-based indicators, such as: the contribution of a country to the world top-10% (top-1%) of the most highly cited publications, the share of such publications in the country's total output, the highly cited papers index, etc. Relying on them, the author fully discloses the scientific «offensive» of the «newcomer» countries on the «incumbents» ones (e.g. China on the USA, South Korea on Germany, Iran on Russia), the phenomenon of Singapore as an effective producer of highly cited publications on the carbon nanostructures, and international co-authorship in the top-1% segment of the most cited articles. Russia's positions are studied in detail, the main domestic research participants are established, and based on bibliometric criteria the center of scientific excellence in the field of graphene is identified. The paper characterizes the supporting role of a number of national science foundations in the NT carbon direction development using data of WoS. The author used the Science Citation Index Expanded database for the initial bibliographic sampling; information of science foundations of Russia and the USA, as well as patent organizations of Russia (Rospatent) and the world (WIPO) for additional comparison.