but where does the money come from? it seems like a good way to avoid regulatory scrutiny if your acquisition goal is to simply exit a competitor from the market.

The money comes from investors. Private Equity basically works by taking money from investors to buy companies and turn a profit with them, paying back the investors when they do so (it's a very illiquid and risky investment, so the advertised returns tend to be higher, but it does seem like a lot of firms are struggling to actually make it work).

Basically a loan.