THE United Nations Security Council today begins the process of choosing a new UN secretary-general. It hopes to send a name to the General Assembly for the formal appointment no later than Oct. 15. Secretary-General Perez de Cuellar's five-year term expires Dec. 31.Given the expanded responsibilities and expectations now attached to this office, it is regarded as a fateful choice. In the absence of any prior screening, there is little time to decide. In fact, France and the Soviet Union have again been talking about persuading Perez de Cuellar to stay on for two more years. Africa has submitted an official list of six nominees. Several private citizens have nominated themselves. Dozens of other names have come up in speculation. Everyone wants some independent man or woman who can carry the political load and also tighten up a flabby, disjointed, and often wasteful UN administration. But thereby hangs a complex and contradictory tale. The secretary general is the leader of what is called the UN system. This embraces the Secretariat with headquarters in New York, 14 specialized intergovernmental agencies, and approximately 150 bodies in the economic and social fields where some 80 percent of the UN's work is done. Altogether, the system employs some 50,000 officials and staff in roughly 620 foreign headquarters and field offices around the world, and spends anywhere from $4 billion to $6 billion a year. It seems impossible to pin down an exact figure. On paper, all is well. The General Assembly, comprising the full UN membership (soon to be 166 states) is the supreme policy body setting the basic goals. The Economic and Social Council is charged by the UN Charter with recommending policy on international economic, social, cultural, educational, health, and human rights matters. (Just as the Security Council is given prime responsibility for the maintenance of international peace and security.) The secretary-general is to coordinate the whole in compli ance with the Assembly's directives. In fact, the system is a patchwork shambles that has grown like Topsy for 45 years. An official study in 1969 called the UN's economic development aspect a "non-system," lacking a "central brain." Nothing has changed. Governments continue to demand greater coordination, rationalization, and economy; yet, the fault is in themselves. The UN, like any club, is no better than its members. In the General Assembly, too much of the annual session's 150 point agenda has been described as obsolete, inactive, and overlapping. Debate covers the same ground in several forums. The Economic and Social Council, with 54 members and an amorphous jurisdiction, has no authority to make any UN-related body accept its guidelines. Specialized agencies, such as the International Labor Organization (ILO) and the International Telecommunications Union (ITU), are totally autonomous and do what they please. Recently, the Assembly, in an act as astonishing as it was ineffectual, officially rebuked the ILO and the ITU for feathering their employee's nests in a time of fiscal stringency. Four bodies deal with world food. One of them, the Food and Agriculture Organization (FAO), is widely criticized as utterly mismanaged. The United States, in protest, has cut its contribution to the FAO budget; it has, for the same reason, left UNESCO, the UN Educational, Scientific and Cultural Organization. Economic developm ent agencies fight over turf and together are at war with the UN Environmental Program in the classic conflict of green fields and smoking chimneys. Aid agencies jostled for a share of the action in the Kurdish refugee crisis. THE secretary-general has no power to knock heads together. His efforts at coordination are routinely ignored. Even his management of his own bailiwick, the Secretariat, is undercut by the member states. In the Assembly, the majority sets up pork barrel programs intended to escape his control and restricts important personnel appointments. All demand jobs for their nationals - some qualified, some brothers-in-law. The major powers, including the US, are thinking of saddling the next secretary general with a cluster of four top officials intended to relieve him of part of his burden but more likely, thereby, creating another clique of semi-autonomous bureaucrats. What all, including the small, developing countries, want is an honorable, competent, independent person - not too independent of them. The US calls for a "unitary UN," pulled together to overcome the confusion, waste, and redundancy of the present system but not enough, as Assistant Secretary of State John Bolton put it, to be "tightly orchestrated by a political majority in the General Assembly." Lots of luck.