If your scope isn't well polar aligned but is well autoguided, the star you are autoguiding on will be a point, all other stars will trace circles around that star.
How long? Depends how inaccurate your polar alignment is, the focal length of optics, distance of the guide star from the image field, and length of exposure.
Celestial wonders has an online calculator that will let you put in the values
http://celestialwonders.com/tools/ro...ErrorCalc.html
Examples
ED80 600mm focal length,
polar align error -1 degree from true pole
guide star 2 degrees from image field
5 min exposure
Trail length 8 microns (about 2 pixels)
ED80 600mm focal length,
polar align error 5 degrees from true pole
guide star 10 degrees from image field
5 min exposure
Trail length 40 microns (about 10 pixels)
Telephoto lens 200mm focal length,
polar align error 5 degrees from true pole
guide star 10 degrees from image field
5 min exposure
Trail length 67 microns (about 16 pixels)
You can do your own experiments with different lenses and parameters.
Joe