Have you ever seen a large corp and how inefficient they are? The only reason they can remain large is because they can afford to buy politicians and legislation to keep their competitors small. Big Corp creates new regulations to protect their business, the most clear examples are in telecommunications and the music/movie/copyrightable industries.
If we removed more regulations today, the big corps would try and place them back to destroy their competition.
In a purely capitalist society wealth (power) accumulates at the top. Money creates money so whomever starts out with the most money tends to win. This is why highly capitalist societies turn into Dubai, with an ultra rich ruling class and a serf/slave class with little in between.
Just as an FYI (and apologies if you are already aware of this), but Standard Oil had already lost about ~25% of it's market share by the time it was broken up. Rockefeller had no influence in Texas and California where the wildcatters had moved to and found oil.
A regulation-free system is not a stable equilibrium, so the conclusion will not be regulation-free.