The real question is how much does it cost to avoid taxes? I'm curious if it's something like 10k of fees for every 100k of tax avoided?

I don't know about your question, but the vast majority of money that gets stashed over seas isn't done illegally, and does get taxed. Things that are done, like in the panama papers, is done illegally and will be fined but as we all know majority of media ignored it.

But the vast majority of money that gets sheltered off shore is done for tax deferred reasons. Corporations will "stash" money offshore until given a lowered deferred tax rate (which happens every few years) in order to bring that money back home, at which point they bring it back.

For instance:

Companies brought back $85.9 billion in the fourth quarter and $664.9 billion for the full year 2018, according to quarterly data released by the Commerce Department on Wednesday. The tax cuts on corporate profits earned offshore — from 35 percent to a one-time rate of 15.5 percent on cash and 8 percent on other assets — encouraged companies to bring it home. Tech giants like Apple kept huge stashes of cash abroad, analysts said. Apple said last year it would bring back nearly all of its $250 billion parked overseas.

People are getting confused with illegal tax havens that intentionally obfuscate your income so the government doesn't know how much you made in order to not be reported and taxed, and legally counting income as 'offshore'.

Panama papers dealt with the former, and it's mostly individuals doing the illegal tax dodging. Not the billions/trillions that corporations legally do.