The answer is complicated. And I hope it will answer future questions like that. But please edit question so it has relevance (add something like: battery life and life cycle)
First you have to have an idea how battery works. In short, it is an chemical compound container, which generates current from chemical reaction. That it can be charged and discharged is beside the point. Since it is an chemical reaction device it will get used up - that is: will store less and less charge.
Battery when charges generates heat. The higher the temperature of battery during charge the shorter it's lifespan will be. In short: high temperature kills battery. By "high" it's understood anything above 40 C (104 F) degrees.
But battery is not the only source of heat in a portable computer (no matter what kind).
So, if you roaming a lot and using your machine a lot and - obviously - will be charging it a lot WHILE SIMULTANEOUSLY using it, you will eventually trash your battery. Which is sort of EXPECTED.
On the other hand, if you remove your battery you better make sure it is half-charged or so (40% charge is best) and you still have to discharge and charge again every 2-3 months or so for it to keep it's nominal capacity. because unused battery will get used also (remember? chemical reaction?).
There are suggestions - not stupid, let me add - that unused battery should be stored in the fridge (not freezer, though), but... Exactly: but.
So, if you use your machine a lot when connected to charger, but the battery is fully charged, it doesn't really matter if you remove it or not. It's simply because the battery is on support current only then and is not being really charged, thus not really impacting it's condition. Better to have it, because machine is better balanced and more stable with it.
And final answer is this: if you want your battery to last as long as possible, you should ALWAYS charge it with computer powered off, so the battery can be COOLED by the bulk of the computer rather than extra heating it.
And the (sort of) explanation for that is: since battery is a chemical reaction device it is EXPECTED it will loose on average 20% of it's nominal capacity a year. Depending on actual, individual usage way more or way less. Mine, for example, are at 20% nominal capacity after 2 years, as I'm very aggressive roamer.
There's no way around it, actually. That is also, incidentally, why the battery is covered by 6 months warranty at best by manufacturer. And that's why the batteries are cheaper than before and why there is huge market for non-genuine replacement parts like this. I recommend to bite the bullet and just calmly await time when battery needs to be replaced, then find non-genuine product with lots of positive comments on ebay.
So, armed with that knowledge, you have to decide for yourself what to do. You can, usually, open your machine and remove battery, but with tablets it's delicate (although rather easy) job. Is it worth the (minimal) risks? And you will handicap yourself - ending with a tablet you cannot quicky take with you, even to another room is for me too big a utility loss. But it's your decision.