Well what are the alliances. The US and Britain would probably win anyways
It's very up-in-the-air about who's on what side, but there are a few basic guidelines we can predict. France, Germany, UK, and USA will be on one side of the conflict. The probable other side would be... China, North Korea, or maybe Middle East alliance #33.
Russia is a wild-card. It would either see WW3 as a re-opening of old wounds with the Western European nations, or Russia could see the conflict as a chance to redeem itself in the eyes of its neighbors. Russia has had to prove itself time and time again over its 2-millennial lifespan to countries like Sweden, France, Germany, Italy, Austria-Hungary, Britain, Spain, and Japan that its a competent country in terms of economical, political, and social practices.
The probable scenario would be as such - China and US get into heated arguments over... probably Korea, but China has a habit of keeping NK under a leash, but its the most probable. It could also stem from a mega-capitalist or mega-communist rising in the USA or PRC respectively and declaring war. (This is most probable, seeing as how Your Friendly Neighborhood Satanist is destined to become President of the USA, and if you're American, you know one thing, You. Hate. Commies.)
The UK joins in with the US almost instantly because of the "Special Relationship", quickly followed by past members of the British Empire (South Africa, India, Australia, Canada, etc.) and the rest of Western Europe. Russia and Mongolia might also jump into the fray against China, and Pakistan might invade India if the country joins the other Commonwealth nations.
Why Mongolia? Why Russia other than the above stated? And why Pakistan?
Mongolia has had a hatred of China since the get-go. Genghis Khan spit on the Chinese-Mongolian border back in the 1400's after the Emperor of China suggested the country to the north capitulate. Ever since then, Mongolia's greatest conquest was its southern neighbor, quickly followed by the fall of the largest empire the world has ever seen. Tensions followed throughout History, and spiked again once Mongolia became a Communist country alongside China. However, Mongolia was Soviet Communistic, not Maoist Communistic. The difference, I do not know. All I do know is that the USSR and the PRC hated each other just as much as the ever-famous USA-USSR rivalry.
Mongolia was numerously considered to join the Soviet Union, but it never happened. When the USSR collapsed, Mongolia quickly became a democratic-Capitalistic country.
So why Russia? See above. The lesser-known PRC-USSR rivalry was nearly as intense as the USA-USSR one, and the wounds between these two countries probably haven't healed as well as the Russia-US considering the different government and economic types.
Why Pakistan? The country considers themselves cheated after Britain drew up the final borders for the newly-formed nations in the Indian-Peninsula area. Pakistan is also a predominantly Muslim country, and if you think Americans hate Muslims, you haven't seen Hindu India. Many years ago, the Mughal Empire dominated India with an Iron-Muslim fist. The empire was overthrown, and the Hindus were back in charge.
What could we see come from this war? Probably severely limited Nuclear shelling. The countries in conflict acknowledge the concept of Mutually Assured Destruction, with the exception of potentially North Korea, but pressure from the PRC could prevent it from starting full-scale nuclear combat. If Russia joins the fight against China alongside Western Europe, the Commonwealth, and the US, then China, North Korea, and Pakistan have to look down the barrels of the combined two largest nuclear stockpiles in the world.
Again, the nations in conflict are smart enough to acknowledge MAD, so the use of Nuclear Weapons is extremely slim.
If the situation gets dire enough, we could see the return of the Japanese Armed Forces, but again, extremely unlikely in the extremely unlikely event of there even BEING a World War III.
World War 3 has many unlikely events within itself, and these events are made even more unlikely with the actual war itself. World War III 's chances of happening diminish every day. The world is extremely interdependent, and in the near future, no one nation could fund missions off our planet, the only sure-fire way to preserve and continue the Human species (but we already had that thread).
World War III? If it happens, look at what the nations of China, North Korea, and Pakistan have to fight. The sole superpower on the earth, joined by a collection of the most powerful European nations on Earth, combined with the potentiality of a Northern Front against the largest nation on Earth.
Capitalistic-Democratic-Republics win again!
-Chillz