The reins held by the railroad magnates attach not only to the trains but also to the tracks and the railroad station. what does this convey about the magnates' control of the railroads?

The cartoon showed that Cornelius Vanderbilt had total control of the railroads and was able to do (and charged) whatever he wished for the use of them. This was the state of transportation in the late 19th-century: a few large companies were in total command of the railroading industry and were able to set rates that other, smaller businesses were required to pay in order to stay solvent.

Dpolitical is the answer