Hi,
Conversion to an alternator is pretty easy. martx-5 gives you a good overview about using the very easy-to-find and inexpensive Delco unit (I bought a rebuilt one locally for $50-55 without a core to exhange). I've got one installed in my TR4, which is identical to your TR3 as far as engine and generator. Biggest problem you might have is finding enough room for the alternator next to the inner fender on your car, so you might keep looking for others who have converted a TR3 specifically.
Do add wiring to accomodate the additional power output. Dan Masters surely addresses this, but I think it worth repeating here. You can either replace the main wire with something much heavier or double up with a second wire to carry all the extra juice. The single original wire just isn't heavy enough to carry the load.
Yes, you'll need to convert the alternator to use the wide belt, if the route you are choosing is to keep the original style belt. I converted to a thin belt at the same time (less drag on the engine, easier on the bearings in the water pump and alternator) and it all was part of installing an electric cooling fan on the radiator, completely deleting the existing fan from the front of the engine. So, my installation also includes a harmonic balancer/crankshaft pulley combo that replaces the fan extension (which originally also served to help dampen engine vibration and is important to keep, even if the fan is removed, unless a true dampener is installed in its place).
There are some photos of the installation of the alternator on my TR4 engine, at the link below, if you want to see how it looks.
If you search the archives here you will find several previous discussions with more details about converting to an alternator.
There are also several very detailed and well illustrated articles out on the Internet that cover the subject. If you do a search, I suggest you look also for TR4/4A, since the engine, generator & mountings are all essentially the same.
/ubbthreads/images/graemlins/cheers.gif