Looking on the internet deeply has found these results:

all over the world is the most popular phrase on the web.

all across the world 111,900,000 results on the web	all over the world 1279,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
So you can have lots of small facilities spread all across the world. Far from being beaten, militant faith is on the march all across the world, with terrifying consequences. Seven of them, all across the world. Mr President, next week, all across the world, people will be celebrating the life of Scotland's national poet, Robert Burns. You've made thousands of enemies all across the world. Every meal you eat contains ingredients from all across the world. Demons exist all across the world in their varying different forms. Vannacutt was a big art collector, traveled all across the world.	It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

all across the world

111,900,000 results on the web

all over the world

1279,000,000 results on the web

More popular!

So you can have lots of small facilities spread all across the world.
Far from being beaten, militant faith is on the march all across the world, with terrifying consequences.
Seven of them, all across the world.
Mr President, next week, all across the world, people will be celebrating the life of Scotland's national poet, Robert Burns.
You've made thousands of enemies all across the world.
Every meal you eat contains ingredients from all across the world.
Demons exist all across the world in their varying different forms.
Vannacutt was a big art collector, traveled all across the world.

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.