By POE do you mean PEO aka poly ethylene oxide aka PEG? POE can apparently also mean polyolefin elastomer, which is confusing.
Assuming I read you right, C16H33 isn't really a polymer, its too short. You can just BUY pure C16H33 (hexadecyl or cetyl) with a terminal alcohol, carboxylic acid, amine, etc. After about C24 or so you do have to do some sort of olefin polymerization and get a reactive endgroup which is a real technical challenge. The reason we have access to C10-24ish with reactive groups is because biology provides them as part of lipids as esters or carboxylic acids.
Anyways, the way to make an alkane "endcapped" PEG is actually do it backwards. You initiate the ethylene oxide polymerization with the appropriate molar ratio of hexadecanol (C16H33OH). You then stop it with water or methanol, depending on what you want the other end group to be.
You can also start a pegylation reaction with ethanol, then stop it by quenching with excess hexadecanol, but seems messier to me. You have to get the extra hexadeanol out afterwards which could be a pain.