Under a constant flow velocity V, a flexible polymer (in steady state) is expected to display three types of conformation: 1) unperturbed at low V; 2) "trumpet": partly stretched, with certain scaling laws (F. Brochard-Wyart, Europhys. Lett., 23 (1993) 105) at intermediate V; 3) "stem and flower" with a completely stretched portion (the stem) at high V. We discuss regime 3) here. We also consider transients where (starting from regime 3)) the flow is abruptly suppressed and the resulting decay law for the stem is of the Rouse type.