The asparagus fern plant (Asparagus aethiopicus syn. Asparagus densiflorus) is normally found in a hanging basket, decorating the deck or patio in summer and helping to clean indoor air in winter. The asparagus fern plant is not really a fern at all, but a member of the Liliaceae family. When growing asparagus ferns outside, place them in a part sun to shady location for best foliage growth. While the asparagus fern plant may sometimes flower, the tiny white flowers are small and not necessary for the beauty of growing asparagus fern.