The F1 has a huge zucchini plant, but yet she reports not many fruit; "They're little and fall off." Ah, a pollination problem, right up TPP's alley. Garden squash plants are what we call monoecious, one house; they produce two kinds of flowers on the same plant, those producing pollen ("males") and those producing fruit and seed ("female"). They aren't actually male and female, but the explanation takes more effort that TPP has right now. The plants usually start out producing male flowers, they use less energy to make so plants can start flowering at a smaller size. The female flowers are easy to distinguish because you can see the immature fruit below the yellow corolla (right side), which is lacking on the males (left). If not pollinated, no more energy is wasted and the flower aborts. This can happen in a small garden, maybe with only 1 zucchini plant because maybe no males flowers were produced on a particular day. However it also could be because you don't have any bees around to move the pollen for you (or you have left a row cover in place too long keeping the pollinating insects our along with the bad guys). If you lack bees you can pick a male flower, tear off the yellow corolla, and swab the anthers on the stigma of one or more female flowers effecting pollination yourself. This can also happen with cucumbers. Bees visit male flowers and collect pollen as a reward; females flowers have stigmas that mimics the males, thus deceiving pollinators into visiting and delivering pollen. Tricksy plants! Note the flowers are edible themselves, so if you are getting too many squash, try eating some at their smallest stage. For more information on raising squash and their relatives go to Renee's Garden. The image used above is from this site.