It's sad to read the answers here. The answerers treat the question as a joke or have absolutely no clue how WWIII would play out.
First of all it's not a joke. WWIII could very well break out today. Probably won't, but it could. Wars more often than not start by accident. Some nation takes some sort of action that triggers a response that it didn't expect from another nation, and the war begins. EX: N. Korea launches an IBM test shot without telling anyone and the US thinks it's a launch against the mainland and responds with a fusillade of its own IBMs...and WWIII begins when China and Russia join in.
But most importantly the intensity and scope of WWIII will find there are no winners in that horrific conflict. More than a third of the world's population will die of prompt and delayed nuclear effects. The world's infrastructures will be destroyed beyond reasonable repair periods. Starvation, exposure, and disease will wipe out another 1/3 of the population. Only pockets of humanity will survive around the globe and they will be exposed daily to threats that could lead to their extinction. [See source.]
SIRNEM (strategic international relations nuclear exchange model) is a comprehensive WWIII model that was widely used in the 1970s to play out scenarios of conflicts. As a Research Associate with a National Lab that designed, built, and tested nuke weapons, I used SIRNEM results for my studies. There were no winners, no matter what scenarios were assumed.