As far as I know, Grayscale is by far the biggest player in the BTC ecosystem. As per the attached spreadsheet they now control more than 2% of the entire BCT supply. Square is getting bigger, and
other competitors just started taking steps in this direction, given the huge amount of money to be made. Yet, the pressure is not against the newly mined bitcoin, but against the total supply. So a lot has to be done. But nonetheless, I expect this business growing steadily over the next quarters. Remember that bitcoin is still tiny. The entire market cap of Bitcoin is equal to the market cap that Amazon raised in the month of July only(more or less 220 billions).
Coinbase holds around 1 million coins, that's 4.7% of Bitcoin's supply. And technically, Satoshi also owns 1 million coins, so he's also the biggest player in Bitcoin ecosystem, though he's disqualified cause he's inactive now.
Still, holding 2% of supply is pretty big. I wonder if there's any entity that holds 2% of all gold in the world?
Easy answer to this.
Approximately all the gold mined in human history is around 200,000 tonnes, that could be concentrated ona 22 meters cube

Total above-ground stocks (end-2019): 197,576 tonnes
- Jewellery: 92,947 tonnes, 47.0%
- Private investment: 42,619 tonnes, 21.6%
- Official Holdings: 33,919 tonnes, 17.2%
- Other: 28,090 tonnes, 14.2%
- Below ground reserves: 54,000 tonnes
https://www.gold.org/goldhub/data/above-ground-stocksSo central Banks are the Official Holding part, around 34,000 tonnes, andare for sure the most concentrated.
On the officially reported holdings of
Gold Reserves chart, the US Treasury is stated holding around 8,000 Tons of GOLD: that would be around 4% of the total supply. Second place for Germany, with 3,800 Tons, or 1,7% o the total supply.
So the answer to your question is: "Yes, there is only one institution controlling more than 2% of the total Gold Supply: the US Government".
When speaking about "entities" I was actually referring to "financial instuments" controlling bitcoins, e.g. ETF's, ETP's , pension funds, or even
listed companies, holding Bitcoins.