What is the best way to get rid of small trees?

This is likely caused by roots left in the ground from another tree that was cut down. There are several options here. UT Extension Agent Booker T. Leigh recommends using a stump rot to kill the existing roots. UT Extension Agent Chris Cooper recommends cutting the sprouts and then painting the cut ends with a 41% glyphosate solution.

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Controlling unwanted trees and shrubs