With carbon particles we analyzed patterns of growth in Acetabularia acetabulum (Lam.) P.C. Silva, a giant unicell famous for classic development studies. We focused on the stalk apex, which generates the stalk, whorls of hairs, and whorls of gametophores. To gain visual and physical accessibility, we amputated the youngest whorls of hair and the original apex and performed experiments on the apex that regenerated. Video analysis indicated that most growth occurred near the tip of the new apex. Less growth occured throughout the cut-interwhorl. We also analyzed cell wall thickness along stalks cleared of cytoplasm. Correlating growth data to wall morphology suggests growth near the apex may be proportional to stress on the cell wall. We propose that turgor-pressure wall stress modulates local apical cell wall growth rates. A supplementary model, relating cell wall curvature and growth rate in the cut-interwhorl, characterizes how the stalk's final dimensions and nearly cylindrical shap may arise. See http://faculty.washington.edu/mandoli/vondassow for supplementary data, analysis, and mathematical appendices. We believe this is the first quantiative description of apex morphogenesis of A. acetabulum.