What tends to trigger anger outbursts in children?

Setting no limits. Children need boundaries. When none are given, they become spoiled, angry, out of control, hating the world and everyone in it. Responding to every outburst with a calm, "no" and a reasonable punishment will reinforce there are limits/boundaries that are not to be crossed. They will learn not to do that. Calm patience and consistency is all you need. More about teaching the adult then the child.
Negative attention- seeking behaviors' purpose is to attain a desired object or preferred activity or to avoid a non-preferred task. Start time-out at 18 mos. Learn to do it correctly as a tool to ignore negative behavior effectively, the only way to "make" it go away. The behavior will escalate at first in an attempt to elicit negative or positive attention from you, then extinguish if you consistently ignore it.
Stress and impulsive. Children are going through developmental maturation. Their brain and body is growing and developing "control mechanism". Generally when a child is overwhelmed by more stress than he or she has capacity to deal with, the result can be an anger outburst. On the other hand, a child may "hold anger inside" and this often will develop into depression.