cooking vegetables for mashing

cooking vegetables for mashing

Inspired by some of the answers and comments on a recent question on
boiling potatoes whole or diced, I'm curious:
What's the best way to cook a combination of vegetables to be mashed? I'm
thinking of a subset of potatoes, turnips, rutabagas, parsnips, carrots,
and anything else that sounds good. Obviously if boiling, one wants to
avoid waterlogged vegetables, but the cooking times of the various
vegetables are different. Is there a reliable way to cook everything
together (at least for some subsets)?
Edit: As mentioned in the comment below, I know that the best one can do
may be starting with the longest-cooking vegetables and incrementally
adding the rest. What I was wondering was things like if some or all were
better baked, or if boiling is good, if some besides potatoes are better
boiled whole...