To control weeds and reduce moisture loss from the soil during hot, dry periods, spread a layer of organic mulch 2 or 3 inches thick on the soil under the poplar tree.
Sassafras trees grow best when they have a good water supply and soil that drains well. Water newly planted trees regularly for several weeks until they are established. Otherwise, during periods of normal rainfall it is not necessary to supplement their water. While they are able to manage considerable drought in fields out in the wild, it is beneficial to water those poplars in the yard when rainfall is scarce.
When the tree has been in place for at least six months, sprinkle some granular slow-acting fertilizer formulated for trees and shrubs on the mulch for the rain to soak in.
Little pruning is required. Remove awkward and damaged growth as needed. If a single-stemmed specimen is desired the suckers should be removed while they are small. If suckers are left in place a dense, but not unattractive, colony will form.