What was the goal of trust-busting in the early 1900s?

To impose a regulation on a certain amount of American businesses or definitely dissolve them.

Explanation:

In the last part of the 19th Century and first part of the 20th Century, a big part of the United States went through a process of industralization. As a result, big businesses emerged. Some industries turned to big companies which achieved superiority over their competition by associating with each other, becoming monopolies. This is what trusts are.

Reformers of the Progressive Era considered them to be detrimental for the American economy and its costumers. Since there was no competition, trusts could determine the prices at their own will. So, these Reformers appealed to the law to introduce what it would be known as "trust busting" in order to dissolve them.

to extend a country’s power and influence