'Politics' is very vague word, of course, so it's necessary first to define those aspects of the existence of a nation state and its citizens that can be treated as 'political' for the purposes of this analysis.
The 'governance' of a country is a first approximation: the tasks which are subject to the political process include the making and upholding of laws, including the legislature and the judiciary; the raising of taxes and debt; the formation and carrying out of spending programmes; issuance and maintenance of a currency; defence; the conduct of an administration; the provision of services including education, health, welfare and pensions.
While that may be a list of the roles of a modern nation state, it would have looked very different two hundred years ago, let alone 1,000 years ago. The State has tended to accrete roles over many hundreds of years. However in the last 50 years there has been a tendency for the list to shorten again rather than lengthen, even if the total amount of money raised by the State has continued to increase as a proportion of national wealth in almost all countries, so that considerable parts of the administration of a country as defined above can by now be treated as part of non-governmental economic management.
The formation and carrying out of spending programmes, and the conduct of an administration, while crucial roles of the nation state, are functions which have to be performed by any organization at whatever level of 'globalization' it may exist; thus they don't call for analysis as part of the globalization process. Many executive agencies of government, as they are trendily termed, have in fact been privatized or at any rate made independent of political control in a number of countries. It is likely but not certain that this process will continue. Whether or not such functions will become globalized in due course is a harder riddle to solve.
Most liberal economists agree that education, health, welfare and pensions should be privatized to a greater or lesser extent (mostly greater!); but governments are extremely unenthusiastic about it, for doctrinal or 'nanny state' reasons. It is clear that while nation states still have a firm grip on the delivery of these services, there is growing demand among practitioners and users (parents and patients) for more choice. There is economic logic in it, as well, and the sheer cost and inefficiency of state provision in these areas, combined with growing affluence on the part of consumers will combine to drive such services gradually into the private sector, at least in richer countries.
Of course it is true that every year the absolute number of 'not better off' people in the world is growing, so that even if many more people move to private provision of education, health, welfare and pensions, in the short term they will represent a diminishing proportion of the global population. However this is only a short-term situation: within thirty years the enormous populations of China, India and other rapidly developing countries will have lifted themselves out of poverty, and we will enter a phase during which the number of poor people will decline, both absolutely and relatively. Given the speed with which understanding of economic mechanisms is advancing worldwide, poorer countries may at least be spared the socialist experiments that have been imposed on today's economically advanced countries, and will perhaps move directly to more market-oriented systems for the provision of social goods.
Chapters One and Two have described the processes by which economic management, and the delivery of health, welfare and education, as 'cultural' goods, are gradually becoming globalized; they can therefore be excluded from this Chapter's consideration of 'political' globalization.
The residual governmental tasks, then, may eventually be defence, monetary and fiscal affairs (issuing, raising, borrowing and spending money), and the law. Chapters Three described the globalization process in fiscal affairs from a taxation perspective, and Chapter Four described the globalization of the law and dispute resolution; it remains in this chapter to deal with defence, the monetary aspects of fiscal affairs, and to review the international organizations which are taking shape as the building blocks of a globalized polity of the future.