Did Cincinnati,New Orleans and Texas Pacific had any relationship with the Texas & Pacific railroad.
No, so far as I know, it was the project of the city of Cincinnati (which still owns the road) to reach Chattanooga. In cooperation with the Alabama Great Southern and the New Orleans and Northeastern, the Queen and Crsecent Route was formed, linking the Queen City with the Crescent City.
The actual CNO&TP as ‘Queen and Crescent’ Route was the invention of English bankers. Had it actually decided to run through Texas, it would have needed a subsidiary – like all other railroads in Texas at the time – actually headquartered in Texas in order to do so legally.
As noted, much of the ex-CNO&TP route is still leased by Cincinnati to the Southern (one of whose most famous presidents, a Connecticut Yankee, in fact came from the Queen and Crescent in the years before WWI) and the lease is apparently up for renewal or renegotiation in 2024.
I believe that CNO&TP continues to exist as a corporate entity since it holds the lease of the Cincinnati Southern, which is wholly owned by the City of Cincinnati.