Fabricating vertically ordered and etchable high aspect ratio nanodomains of block copolymer (BCP) thin films on diverse substrates via continuous processing dynamic cold zone annealing (CZA) is particularly attractive for nanomanufacturing of next-generation electronics. Previously, we reported dynamic CZA studies with a shallow thermal gradient (maximum del T similar to 14 degrees C/mm) that produced only BCP cylinders oriented parallel to substrate. Here, we report a CZA utilizing a dynamic sharp thermal gradient (del T similar to 45 degrees C/mm) (i.e., CZA-S). This method allows for production of etchable and vertically oriented cylindrical domains of poly(styrene-b-methyl methacrylate) in 100-1000 rim thick films on low thermal conductivity rigid (quartz) and flexible (PDMS, Kapton) substrates. Competing substrate wetting interactions dominate BCP orientation in films below 100 nm while broadening of the thermal gradient profile in films thicker than 1000 nm leads to loss of vertical orientation. An optimal dynamic sweep rate (similar to 5 mu m/s) produces the best vertical order. At too fast a sweep rate (>10 mu m/s) the BCP film ordering is kinetically hindered, while at too slow a sweep rate (<1 mu m/s), polymer relaxation and preferential surface wetting dynamics favor parallel BCP orientation. Equivalent static gradient conditions produce vertically aligned BCP cylinders only at the maximum del T. CZA-S mechanism involves propagating this vertically oriented BCP zone across the sample.