Topoisomerase I will relax negatively supercoiled plasmids. There will be some variation in the linking number of relaxed DNA molecules, which will be distributed around the most preferred conformation. The difference in energy between DNA molecules with different linking numbers is quite small and they will distribute around a mean. Therefore, on an agarose gel without ethidium bromide, a distribution of bands will be seen even for a complete reaction. These bands should all still run slowly and are easily distinguished from supercoiled plasmids.