Linearized DNA occurs when the DNA helix is cut in both strands at the same place. Linear DNA generally migrates between the nicked circle and the supercoiled forms. However, it may also migrate the same distance as nicked circle — it migrates as predicted by the length of the DNA (as compared to the MW markers). You can identify the linear DNA form on an agarose gel by comparing uncut plasmid DNA with a sample of the plasmid that has been linearized using a restriction enzyme. If you get linear DNA when you are hoping for supercoiled (e.g. after a plasmid prep) it is due to nuclease contamination or harsh treatment during purification.