A GP (searcher/sponsor) can recap their way to majority control (>50%) of a successful deal, even with $0 initial equity.
Steps:
(1) The deal has to go well and provide investors with a 1x + Pref ROI either from cash flow or a dividend recap. At this point, the GP is "in the money", where they collect 20% (or whatever the carry is set at) of each incremental equity dollar.
(2) With certain legal structures, your carry is actually vested stock options, which means you own a % of the company. This is the easiest route (legal & tax), as you now own 20% of the actual shares.
(3) The company can repurchase shares from LPs who are willing to sell. You negotiate a FMV share price and offer it to all LPs. Cash flow from operations or a dividend recap credit facility are the two sources of cash.
Example: Through vesting (by providing 1x + pref ROI), GP owns 20% of the shares (let's say that equals 2,000,000 shares). Of the remaining LPs, who own the other 8,000,000 shares, let's say 90% of them decide to sell their shares back to the company. So, the company purchases 7,200,000 shares (by worsening its balance sheet). There are then 2,000,000 + (8,000,000 - 7,200,000) = 2,800,000 shares remaining. The GP owns 2,000,000 (71.42%) of these.
This feat was accomplished by Dan Chetrit (though the numbers above are illustrative). In his case, the majority control enabled the removal of the full-time attention clause of searchers, so they could start diversifying their time towards building a portfolio of companies like an independent sponsor.
Check this week's episode of the Minds Capital Podcast.