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fast growing privacy trees
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This requirement leaves the list pretty large.
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that the deer will not eat...
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This shortens the list considerably.
Deer love the tender new growth of darn near anything deciduous. Maples, oaks, hickory, ash, walnut, elm, poplar, aspen, fruit trees....... deer love them all.
You don't say where you are or what exact purpose you have in mind for these privacy trees, but I'd say your best best would be an evergreen of some kind.
Columnar junipers and cedar trees grow fairly rapidly and will form an effective wind and privacy barrier when planted close together. The junipers have a spikier foliage and will tolerate harsher conditions than most of the softer-leaved cedars. Birds love the fruits and seeds of both. The cedar will provide a sweet aroma when planted in quantity. Species of both types will usually max out at 20 feet.
Another option could be the slower growing white spruce. It will form an impressive thicket if planted tightly. Spruce can reach heights of 75 feet when mature.
The evergreen yew tree might be an option if your soil and sunlight conditions allow. Yews have a very soft evergreen leaf and can be trained to form a very dense hedge.