This is correct. They are essentially a competitor of Vanguard. It's amazing how many people think they're some kind of hedge fund or prop shop making directional bets and gambles.
How do you think it is that Blackrock only owns 6.79% of Blackrock?
When you figure that out, you will have achieved enlightenment and be able to answer your original question.
As of the last time I checked (several years ago), they had over 27T Euros of assets under management.
Their competitor in the US is Depositary Trust Corporation (DTC), and last I checked they had over one quadrillion dollars of assets under management.