kryogenik

I've just bought a new all singing all dancing laptop. It's got a lovely 17" widescreen and it's a battery drinker!

Now, I've had my old lappy for 7 years, and always, always ran it on AC.
The few times I've had to use it on battery it's lasted about a nanosecond..
I've been led to believe this is because I've always ran it on AC and never on just battery - and/or always ran it with the battery connected when using AC and that's what's done for the battery.
As the old lappy battery is shot and I seldom used it for portability (would be embarrassed anyway!) I didn't care much, but I'm really concerned about screwing up the battery in this one as I will almost certainly need it for portability. I've Googled loads and found stoic arguments in both camps - one saying it's OK to run with battery in and AC in but occasionally discharge the battery by running on battery only, the other side saying big no-no as I would be effectively topping up the battery all the time - with this in mind, I've pulled the battery out, paranoid that I'm going to kill it.

Ideally, I'd like to alternate between the two as the lappy runs much cooler on battery. When plugged in the fan's kicking in a bit too often. But, I would prefer to leave the battery out if I'm going to be using it unnecessarily and killing it's life span.

Anyone have the insight to tell me once and for all what I can/can't should/shouldn't do? The battery is a Li-Ion type.

TIA