They would still have business relationships with the other entities they were split from; they'd just be only business relationships, done in public and appearing on the balance sheets, and able to be regulated "between."

An example of the type of business relationship Warren probably wants to encourage: the way Google pays Mozilla to keep Google Search as Firefox's default search provider.

So, if Google were split up into Google-the-search-engine and Google-the-ad-agency, Google Search's main source of revenue would still be from ads—but it'd be via the separate company of Google Ads, paying Google Search for ad placement.