A new urban revolution begun in the second half of the XX century and it is going to challenge the relation between the size and economic role of cities: on one side, the last decades have witnessed the emergence and the never seen growth of a number of Mega-cities, with more than 9 million inhabitants, most of them being located in less developed countries. On the other side, the globalization of the post-industrial economy generates a new urban spatial organization where a few number of cities concentrate a disproportionate part of economic power, creation, decision and control. Most of the largest cities are in the less developed countries, while the most powerful world cities are mainly located in the developed countries. It results that size seems to be neither a necessary nor a sufficient condition for obtaining the status of world city. A condition to be a world city is the access to the economic power. A conventional city has a region behind, and there is no region without city, neither city without region. But a Mega city has, at least, a country behind. When in a country there are several Mega cities, competition for the specialization emerges among them. However, within a country, regions are more closely related. But due to the globalization, the rise of high technology applied to the telecom networks, the expansion of the financial markets, generally located around the big cities, together the great multinational companies, and the strong development in multimodal transportation networks, cause a great growth in some places of the World, attracting immigration and amenities. Nevertheless, although it seems to have convergence among the big cities considered in this work, not all these cities are similar. The main aim of this paper is to analyze the comparison between the real convergence-divergence among 50 Mega-cities of the World, and the convergence-divergence among its corresponding countries, using several growth models, studying the possible existence of Clubs convergence among these cities and countries.