Let's take a look at two case studies. It took a lot of effort that began with the Sherman Anti-Trust Act and was litigated throughout the entire Teddy Roosevelt administration before John D Rockefeller's Standard Oil trust was broken up in 1911. Seven major oil companies were created : Exxon, Mobil, Chevron, Sohio, Amoco, Conoco and Atlantic. Since none of these seven companies could monopolize the petroleum market, other oil companies, like Gulf, Texaco, Sun and Marathon had room to grow into much larger companies, without Standard Oil crushing them. This web-site provides more details.
http://www.e-education.psu.edu/egee120/node/226
The petroleum industry has undergone some consolidation in the last 45 years. Exxon and Mobil merged. Chevron bought out most of Gulf oil. Atlantic merged with Richfield and changed its name to Arco. British Petroleum bought out Arco and subsequently bought out Amoco.
The second case study is the break-up of "Ma Bell". Starting in 1974 the Federal government began to bust the American Telephone & Telegraph monopoly. In 1982, AT & T was broken into seven Baby Bells and newer smaller companies were allowed to enter the telecommunication market. Since then two of the baby bells (Bell Atlantic and Nynex) merged and soon merged with GTE, which was the second largest American phone company, back in the days of the Ma Bell monopoly. That company is known as Verizon. Four other Baby Bells: Southwest Bell, Bell South, Ameritech and Pacific Telesis have merged together and call themselves AT & T, but they wisely do not use the Bell symbol as their logo. In 2014, AT & T is smaller than Verizon and there are at least two other large telecommunications companies that compete nationwide with Verizon and AT & T, in the cell phone market.