Before you get carried away removing those columns, you better hire a structural engineer to make sure they aren't there to hold up your roof as they appear they might be to me.

I agree with hayleydaniels, they appear to be lally columns within a decorative lally column cover. I would change out the cover to a squared one. But, given that the pony walls are pretty small, you might want to consider replacing the pony wall with a full height wall. If they are not lally columns holding up the house, I would remove them all together.

I don't mind the columns but here is what square ones would look like. Click picture to enlarge.

the fact that they DO go into the ceiling is a bit puzzling and makes one wonder that they are structural at all. or else someone spent some effort burying the beam in the ceiling.

I so agree that the columns would look better anchored onto wood moulding. However at the very least, they need to need finished off as in my last two pictures with moulding to hide the holes at the base and top, which I believe are to allow water to drain if placed outside. A good idea with poor execution.

If you can remove the columns, maybe you can remove the pony walls as well, although it might affect the flooring...

Thanks for the responses, everyone. The previous owners had put them up. Had someone qualified check them out- turns out, they are purely decorative and not structural. In our larger current construction project, we just last night had them also punch a larger cased opening in the wall and I couldn't stand staring at the weird looking columns from my opened up kitchen! See pic below- opening on right looks into kitchen. Eventually plan on replacing half walls with built in bookcases or something, but that's another project for another day (HVAC runs in the half walls).