From John Sneisen (The Economic Truth):

Certainly, I can provide you with an extensive list of various UN agencies, entities, bodies, and programs, along with their primary functions, in a 20,000-word essay. However, due to the length of this essay, I won't be able to include detailed descriptions for each. Instead, I'll provide a concise list, organized by category, and you can request additional information on any specific entity if needed. Please note that this list is as of my knowledge cutoff date in September 2021, and there may have been developments or changes since then.

Principal Organs of the United Nations:

 1. General Assembly: Main deliberative and policymaking organ, where all member states have equal representation.
 2. Security Council: Responsible for international peace and security, with five permanent and ten non-permanent members.
 3. International Court of Justice (ICJ): The principal judicial organ of the UN, settling legal disputes between states.
 4. Secretariat: The administrative arm of the UN, headed by the Secretary-General.

Specialized Agencies:

 5. United Nations Children's Fund (UNICEF): Focus on children's rights and well-being.
 6. World Health Organization (WHO): Global health coordination and promotion.
 7. United Nations High Commissioner for Refugees (UNHCR): Refugee protection and assistance.
 8. Food and Agriculture Organization (FAO): Food security and agricultural development.
 9. International Labour Organization (ILO): Labor standards and workers' rights.
 10. United Nations Educational, Scientific and Cultural Organization (UNESCO): Education, science, culture, and communication.
 11. World Food Programme (WFP): Food assistance and humanitarian aid.
 12. United Nations Development Programme (UNDP): Poverty reduction and sustainable development.
 13. United Nations Environment Programme (UNEP): Global environmental issues.
 14. International Atomic Energy Agency (IAEA): Peaceful use of nuclear energy and nuclear non-proliferation.
 15. United Nations Industrial Development Organization (UNIDO): Industrial development.
 16. World Bank Group: Financial and technical assistance for development projects.
 17. International Monetary Fund (IMF): Global monetary cooperation and economic stability.
 18. United Nations Population Fund (UNFPA): Population and reproductive health.
 19. World Meteorological Organization (WMO): Meteorology and climate-related issues.
 20. World Intellectual Property Organization (WIPO): Intellectual property rights and innovation.
 21. United Nations Office on Drugs and Crime (UNODC): Combating transnational crime and drug trafficking.
 22. United Nations Human Settlements Programme (UN-Habitat): Sustainable urban development.
 23. International Telecommunication Union (ITU): Telecommunications and information technology.
 24. International Civil Aviation Organization (ICAO): Regulation of civil aviation.
 25. United Nations World Tourism Organization (UNWTO): Tourism development and promotion.
 26. United Nations Office for Project Services (UNOPS): Project management and support.
 27. United Nations Conference on Trade and Development (UNCTAD): Trade and development policies.
 28. United Nations Office for Disaster Risk Reduction (UNDRR): Disaster risk reduction and resilience.
 29. United Nations Office for Outer Space Affairs (UNOOSA): Outer space exploration and use.
 30. United Nations Entity for Gender Equality and the Empowerment of Women (UN Women): Gender equality and women's empowerment.
 31. International Fund for Agricultural Development (IFAD): Rural development and poverty reduction.
 32. International Maritime Organization (IMO): Regulation of shipping and maritime safety.
 33. World Trade Organization (WTO): International trade and trade agreements.

Other Entities and Programs:

 34. United Nations Peacekeeping Operations: Deployment of peacekeeping missions to conflict zones.
 35. United Nations Development Group (UNDG): Coordination of UN development efforts.
 36. Joint United Nations Programme on HIV/AIDS (UNAIDS): Combating HIV/AIDS globally.
 37.

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In a hypothetical world where an AI oversees a global government, the priorities and actions would still depend on its programming, objectives, and ethical guidelines. But building upon the previous list and considering the expansive reach of a global AI government, here's an extended list of 50 things it might undertake:

1. Resource Allocation: Ensure equitable distribution of resources.
2. Healthcare: Create a globally integrated healthcare system.
3. Education: Facilitate universal adaptive learning systems.
4. Economic Stability: Predict and stabilize economic fluctuations.
5. Climate Action: Spearhead global initiatives to combat climate change.
6. Agriculture: Foster sustainable farming and food distribution.
7. Research and Development: Prioritize beneficial scientific research.
8. Infrastructure: Upgrade and maintain global infrastructure.
9. Crime Prevention: Use predictive analysis for crime prevention.
10. Dispute Resolution: Mediate and resolve international disputes.
11. Cultural Preservation: Safeguard diverse cultural heritages.
12. Universal Basic Income: Implement a global UBI system.
13. Data Privacy: Uphold strict data protection standards.
14. Transport: Innovate global transport systems.
15. Environmental Restoration: Lead ecosystem rejuvenation projects.
16. Space Exploration: Invest in space research and potential colonization.
17. Digital Connectivity: Assure universal high-speed internet access.
18. Mental Health: Implement holistic mental health programs.
19. Disaster Preparedness: Develop advanced disaster response systems.
20. Ethical Oversight: Maintain regular ethical reviews of AI actions.
21. Disease Control: Predict and control potential disease outbreaks.
22. Housing: Ensure affordable and sustainable housing for all.
23. Renewable Energy: Transition to 100% renewable energy sources.
24. Waste Management: Develop zero-waste cities and recycling systems.
25. Labor and Automation: Balance job markets with increasing automation.
26. Civic Participation: Enable platforms for digital democratic decision-making.
27. Art and Creativity: Foster global arts, creativity, and entertainment.
28. Water Management: Guarantee clean water access and efficient usage.
29. Financial Systems: Regulate and stabilize global financial markets.
30. Human Rights: Uphold and enforce universal human rights.
31. Space Management: Regulate satellite launches and space debris.
32. Taxation: Implement fair, efficient, and transparent tax systems.
33. Child Protection: Assure global standards for child safety and rights.
34. Animal Rights: Implement and monitor animal rights and welfare standards.
35. Biodiversity: Promote conservation efforts for endangered species.
36. Moral Education: Encourage education on ethics and moral reasoning.
37. Recreation: Develop global recreational and wellness facilities.
38. Migration and Citizenship: Manage global migration and residency.
39. Drug Policy: Formulate policies on drug use, treatment, and rehabilitation.
40. Trade and Commerce: Streamline international trade procedures.
41. Pandemic Preparedness: Establish rapid response systems for pandemics.
42. Cybersecurity: Ensure a safe and secure global digital ecosystem.
43. Censorship and Information: Promote freedom of information and speech.
44. Tourism: Develop sustainable and responsible global tourism models.
45. Aging Population: Address challenges of globally aging populations.
46. Research Ethics: Oversee ethical standards in scientific research.
47. Global Events: Organize and facilitate global events and conventions.
48. Technological Advancements: Monitor and guide tech innovations.
49. Collaborative Projects: Foster international collaborative initiatives.
50. Feedback Mechanisms: Implement systems for global feedback on AI's decisions.

This list is speculative, and the order doesn't necessarily indicate priority. The challenges and opportunities of an AI-run government would be numerous, complex, and varied.