https://www.minneapolisfed.org/artic...or-owned-homes
This is research isold, but it is a good overview of the workings of the market. Currently the number is around 25%, but I think it has become the focus of attention because the large institutions have been the most aggressive in raising rents. And rents are a large portion of recent sticky inflation.
You can also look at Pew Trust, Redfin, they all have research on this.