However, wxfree, if the CTRMA is a subdivision of the state, should we still call it a state highway—even if it's not part of TxDOT? If not, then what do we call it?
A political subdivision is the same thing as a city, county, school district, hospital district, utility district, etc. RTAs and RMAs could be thought of as special utility districts. They could also be compared with counties, the difference being that they have no taxing power, are limited to mobility projects, and have jurisdiction only over the projects that own or operate.
TxDOT is a part of state government; therefore, their roads are state highways. RMA projects are more like city streets and county roads; they're roads of a political subdivision, not of the state itself.
The previous statement is an assumption, true unless modified. I've read that RMAs can run state highway toll roads with cooperation of TxDOT. I have yet to find exactly how that works. I think Cameron County RMA runs SH 550. I have not found and read the agreement between them and TxDOT so as to see how that works. I have looked over the agreement with NTTA about SH 121, and it specifies that the main lanes are removed from the state highway system while the frontage roads are SH 121 and owned by TxDOT. I have not only an interest in roads, but also in law, so these arrangements are of double interest to me.