I don't know which species of Wisteria you have, but I just bought American Wisteria (Wisteria frutescens) and it is supposed to be much less invasive compared to the Asiatic species. I had to take down my Chinese or Japanese Wisteria when a new fence was installed. The native American species is very beatiful too though the flowers are said not to be as aromatic.

Both Chinese and Japanese wisteria are available as grafted plants, but it sounds as though the plant you were given was on its own roots. If that's the case, the answer to your question about "runners" is yes, top growth will continue to pop up, probably for years. Cutting the vine to the ground sends an SOS signal to the roots, so you may notice an increase in the number of "volunteers". Keep an eagle eye out for them and be ruthless in whacking them out or treating them with an herbicide ASAP. Top growth provides energy to the roots, enabling them to continue to spread.

The following link offers some info you might consider.

Here is a link that might be useful: Wysteria Extermination