Blackstone M&A and PE

I remember reading that Blackstone M&A generated revenue by advising Blackstone PE on acquisitions. How does that even work and how does that count as generating revenue? Do the MDs who did the deal get credit or a fee? I'd imagine BX M&A won't have to pitch to get on the deal.

Is it based on the money saved since BX PE won't have to hire an outside M&A advisor (though I'm not sure how this would work since PE would almost always hire a bulge bracket as well for financing reasons)?

How does this work in other firms with two arms (e.g. GS PIA hires GS IBD, DLJ Merchant hires Credit Suisse, BAML Capital hires BAML IBD etc.)?