It is unlikely that avocado trees will bear fruit without cross-pollination between two trees. Though avocado trees have stigmas and stamens, each is available for pollination at different times of the day. This makes it difficult for one tree to self-pollinate. Higher fruit yield is obtained with two trees.
Avocado trees come in two varieties. Blooming in the morning, type A trees show their female stigmas first. The flower then alternates and shows its male stamen upon blooming during the afternoon of the next day. Type B trees are the exact opposite. They open to show the male stamens in the morning and then proceed to show the female stigmas during the afternoon of the next day.