I agree with unclesyd and deanc. We have thousands of 3/4" connections, usually a 1/2 coupling. I don't have TEMA handy, but didn't TEMA require auxilliary connections in heat exchanger nozzles? We often have a 1" and a couple of 3/4" connections in our HX process nozzles. These are usually plugged and provide another leak point and deadleg for corrosion. I'm not a fan. So while there is no code limit on minimum nozzle size, you have to consider the service the vessel will be in. The way I was brought up in the oil refining vessel design business I was tought to use a 2" min nozzle size. Where I'm currently working our standards call for a 2" min (1 1/2" for thermowells) and I fight to upgrade "replace in kind" vessels to that standard. Sometimes we don't due to issues mating up to existing piping. If I'm connecting to existing 1 1/2" piping I make sure we're using LWN nozzles which actually are stronger (in bending) than a typical built up 2" nozzle. I'd attribute the minimum nozzle size to both mechanical strength (some clown will use the nozzle as a ladder etc) and plugging issues. Though I've seen 2" nozzles plugged, its a lot easier to plug up a 3/4" nozzle.
unclesyd- I can't think of any nozzles (of any size) which I've seen which are made of CS or low alloy pipe and Sch 40: With any CA it would be hard to meet UG-45(b)(4), though you could argue that the 12.5% tolerance provides some CA...
jt