Is it possible to charge a car battery using the cigar/cigarette
outlet. If so, what would the maximum charging rate be?.
In most cars, it is possible - the cigar/cigarette/aux-power outlet
usually has a fairly direct feed to the battery, often through a fuse
of its own.
The max charging rate would depend on the vehicle. You'd need to
check the fusebox and/or the owner's manual, and find out what sort of
amperage fuse is used for this feed and whether the owner's manual
says anything about the safety of doing high-current transfers through
this outlet.
The contacts in these outlets are sometimes quite rugged and robust,
and are sometimes pretty wimpy - the latter in cases where the outlet
is intended as a low-amperage auxiliary supply for laptop PCs and tape
players, and not as an actual cigarette lighter.
Trickle and float charging, at rates of up to a couple of amperes, is
probably going to be safe. There are some solar chargers, intended to
provide a low-level float charge for vehicles in storage, which work
this way. I believe that there are some line-powered chargers, good
for a couple of amps, which are used to recharge or float batteries in
cold climates to make sure that they're in good shape to start the car
when the morning temperature drops below zero.
I would not stick a cigarette-lighter connector on the wires from a
stand-alone fast-charger and plug it in... a continuous flow of 20-30
amps is probably quite a bit more than this outlet ought to be asked
to handle.