I'm going to assume you're talking about pruning trees. When trimming a tree branch that you don't want to grow back, you need to cut the branch back to either another main branch or to the tree's trunk. Pruning should be done just outside the branch collar-the swollen, thick area at the base of each branch. Avoid injuring this area, as it is critical to healing the pruning wound.
Never leave a stub. New branches will grow back from around the edges. If you are worried about pests or disease, paint pruning wounds with tree salve (available at garden centers), tar or latex paint. For useful diagrams on making correct pruning cuts, visit the "tree care tips" section at the National Arbor Foundation's website. www.arborday.org
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My mother has always coated the stump of the limb with either honey or mollasses. I recommend Mollassess as it comes in a much large container. Just paint it on like you would a sealant and voila, done.