Answer: The weeping blue atlas cedar is best planted in a large, open lawn area where it can be left to grow naturally; its natural shape is somewhat horizontal and spreading with the branches reaching to the ground.
Any fertilization would be done based on the results of soil tests, your county Extension can help you with the tests and interpreting the results in regard to this tree. During the first few years the tree would need to be watered regularly in times of drought, and a layer of several inches of organic mulch should be maintained over the root area. Any ties or staking materials should be loosened and/or removed to allow for growth. In general, pruning would be minimal. If planted in a suitable location, this tree should not require excessive care.
If you have a young tree you are concerned about, I would suggest you consult on site with a professionally trained and certified arborist who specializes in specimen trees and has experience with this particular type of tree for a detailed evaluation.
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