Well cant speak for your laptop(s) but mine, and others i have had in the past have no issues...
Case One # Leaving the Batt in whilst always on mains = There is chargeing circuit, once the batt is at top capaicty it doesnt charge the batt no longer and the power is supplied directly to the laptop without going through the battery, the second the direct voltage goes, the batt kicks in
Case Two # Leaving the batt out = makes no difference, but leaving the batt in is great for when the power goes, if some one turns the plug off by "accident", power cuts and so you can just get up and park ya self where you want
As i say, cant speak for others, but the laptop i have works like that, i have an acer, we used to sell acers where i used to work, and the acer guy recomended that we dont use the batterys whilst on display as it will make the laptop easier to sell if the battery is brand new when we take it off display. He said however, if its left on charge all the time nothing will happen as the charge is designed to shut off when at full capacity. This maybe true of false but i usually have mine on charge most the time and have done for well over a year and cant see no drop in battery life, i use my laptop for work (7hrs a day) and for games (1hrs a day) and study (2-3hrs a day) and then others use it for bits and bobs. so my laptop is on more or less all day if its been used or not...
Good advice keef with the types of battery, i didnt know that about liIon batteries, and agree that the manual should always be consulted to stay within those tight warrenty terms and conditions...