One of the really interesting aspects of autosomal dominant polycystic kidney disease (ADPKD) is that only about 1% of all nephrons form cysts. You can do the math: if you have about 1 million nephrons per kidney, and 1% of those nephrons are affected, then you will develop about 10,000 cysts per kidney. The reason these patients often go on to develop ESRD is because the growing cysts gradually expand enough to crowd out the remainder of functioning nephrons in the parenchyma.
But why are only 1% of nephrons involved? What's different about the affected nephrons compared to the unaffected ones? One current thought (though this remains controversial) is the "two-hit hypothesis." As described in this excellent 1996 Cell paper , researchers managed to isolate epithelial cells from individual cysts in ADPKD individuals. First, they demonstrated that individual cysts are monoclonal, and therefore derive from a single renal tubular epithelial cell. Then, they demonstrated that within the majority of each monoclonal population, there was loss of heterozygosity at the PKD1 locus. In other words, cysts arise from cells in which a "2nd hit" of the remaining good copy of PKD1 suffers a somatic mutation. This mechanism is much like how tumor suppressor genes (such as APC in colon cancer). The fact that the PKD1 gene is so large (46 exons) makes it especially susceptible to the possibility of mutation. Thus, although the disease is inherited in an autosomal dominant fashion, at a molecular level the cysts themselves are autosomal recessive. This "two-hit hypothesis" is one possible explanation as to why only a small fraction of nephrons ultimately form cysts.