Thank you for your input,
@Rob93.
Just a quick follow up: is there a category name for these companies? I can vaguely remember such a phrase with the word 'vehicle' (EDIT: I believe an SPV?).
My understanding is more so from the fund side, so I'll explain what I know since your understanding is more from the corporate side. Hope it helps!
A PE fund, as you mentioned, is owned by the PE firm and is set up as a limited partnership.
This limited partnership is ran by two key groups of people: (a) general partners; and (b) limited partners.
The limited partners are those that provide the (most) capital (e.g. high-net-worth-individuals, pension funds, insurance funds). The general partners are managers that ran the day-to-day operations of the PE fund.
The critical difference between a GP and a LP is in relation to the extent of liability when things, in essence, don't work out (financially speaking). Maybe an LBO does not yield the expected financial outcome. The GPs are burdened with unlimited financial liability (i.e. there is no limit to the amount they will have to pay out if, for example, an investment doesn’t work out). However, the liability of a LP is limited to the amount of capital they contributed to the fund.
Also, don't forget the classic 2/20 split for general partners. 2% management fees and 20% performance fees (i.e. 'carried interest' - this is how it is usually referred to in the papers).
Apologies if you already have this knowledge and I have insulted your intelligence - you mentioned that your funds knowledge wasn't as strong and you wrote a helpful post to my question too.