Why is acid rain unevenly distributed across the world?

Acid rain is unevenly distributed around the world, and even across some countries, because this weather pattern is highly dependent upon environmental conditions. 
As an overriding factor, parts of the world where rain generally does not fall (such as deserts or the poles) are not likely to experience acid rain. More importantly, acid rain is a result of the environmental concentration of sulfur dioxide and nitrogen oxide. When these emissions are circulating in the air, they react with water and oxygen to create acids. Sulfur dioxide and nitrogen oxide do occur naturally as a result of, respectively, volcanic eruptions and lightning strikes. Human activity and industrialization produce relatively large amounts of these emissions and contribute to greater concentrations of these basic ingredients for acid rain. 
Most of these emissions released into the environment are the result of burning fossil fuels for energy. In areas where many cars burn gasoline or factories use fossil fuels, there are likely to be higher environmental concentrations of sulfur dioxide and nitrogen oxide. These emissions alone aren't necessarily enough to cause acid rain; there must also be sufficient humidity in the air. When acid rain does fall, it isn't always right on top of the people and machines who provided the ingredients. Winds may push acid rain clouds far away from their point of origin, causing trouble for people who may not have contributed to the formation of acid rain at all.
https://www.britannica.com/science/acid-rain

https://www.epa.gov/acidrain/what-acid-rain