To control weeds and grass that compete with young trees for soil nutrients and to help the soil to retain moisture, spread a 2 or 3-inch layer of organic mulch under walnut trees. Use chopped leaves, shredded bark or wood chips in a circle around the trunk out as far as the branches reach. This will also protect the tree from injury by lawnmower or string trimmer.
When they are first planted, young Walnut trees need regular watering from rain or watering system to help them become established. As they mature, they prefer infrequent, but deep watering, so they manage fine without supplemental watering when rainfall patterns are normal. During prolonged drought they appreciate periodic watering. Every 10 days or two weeks run a drip system or sprinkler to wet the soil at least to inches deep, preferably deeper.
Because the nuts on walnut trees use large amounts of nutrients, walnut trees require feeding every year. In the fall sprinkle a fertilizer on the soil under the tree out to 1 1/2 times the distance from the trunk to the tips of the branches (the drip line). Do not allow the fertilizer to touch the trunk, leaves or branches. Use only 1/2 pound or so per tree a year after planting. Increase the amount gradually each year as the tree matures, according to the product label. Do not fertilize when planting a tree, or during its first season.
If intended for ornamental use only, Walnut trees do not require routine pruning. It may only be necessary from time to time to trim off broken limbs, or those that interfere with buildings or power lines. If they are being grown for their wood, these trees must be pruned regularly to shape them. This controls their tendency to branch and fork at will, causing knots and disrupted grains. When pruning for any reason, prune while trees are dormant, in the winter. This will minimize their "bleeding" sap from the pruning wounds.