Can you explain this part more? Does blackrock not invest its own money in deals? And are specific deals specific to blackrock customers or do they just take a percent of their overall holdings and invest them in individual deals?
What the exact flow is will depend ultimately on how the fund is structured. For example, Goldman will run a private equity focussed fund that you can put money in as a customer, so if you did put money in it, they would invest in similar deals on your behalf. Other customers of Goldman may or may not choose to invest in that fund, preferring something like a bond fund or equities fund etc.
It will take away a small percentage of your money every year to pay costs and make its profits, but you will profit from the returns of the investment itself.