There are two basic "sizes" of superchargers fitted to the supercharged FIAT and Lancia models. One is the standard Volumex unit, as found in the production Lancia Beta Volumex Coupe and Volumex High Performance Estate wagon (HPE), as well as the FIAT Spidereuropa, a volumex-equipped version of the popular 124 spider. The other is the larger "ABARTH" branded blower as found in the Lancia Rally 037 and FIAT Abarth 131 Volumetrico. Although it is common in the enthusiasts' circle to refer to the standard blower as "volumex" and the larger blower as "volumetrico", it should be noted that FIAT used the two terms fairly interchangeably. The larger blower is readily identified by the inscription "ABARTH" cast into the front endplate, while the smaller blower reads "Volumex".
Of the ABARTH version, one might find one of two types of blowers. The first has a relatively flat rear housing, and comes from the Lancia 037 application. These cars were fitted with a dry sump, and one stage of the dry sump oil pump was dedicated to scavenging return oil from the blower, which was fed engine oil. On the FIAT 131 version, the motor used a wet sump system, and the blower has a scavenge pump built into the rear housing. It can be identified by a fist-sized lump and additional cover on the blower rear housing.
There is a very rare blower found in the Evo2 version of the 037 Rally works car that is a longer, higher-displacement version of the ABARTH blower, but this one is such a rarity that I've only seen pictures of one, so I will not include discussion of it here, except to note its existence.

Here's a comparison between the standard Volumex units and the bigger ABARTH Volumetrico blowers.
The Volumetrico unit pictured is from an 037, and lacks the distinctive oil scavenge pump
that the FIAT 131 Abarth unit has integral to the rear housing.
Photo by Dave Beale (UK).
VOLUMEX SUPERCHARGER:

The volumex supercharger is a roots-type positive displacement blower. Two hollow rotors trap air from the inlet side against the sides of the rotor housing. This air is then transferred to the exhaust side, where the rotors mesh back together, forcing the air out the back of the unit. It is not a particularly efficient type of blower in comparison to either the Whipple or centrifugal blower types, yet it was used quite sucessfully by Lancia, most notably on the Lancia Delta S4. The S4 was a performance monster that was both turbocharged and supercharged, creating a devastating combination of low end torque and top end power that made it a dominant rally car in its time.
The standard Volumex blower as fitted to the production cars is quite reliable, and can usually be found in good condition after sixty thousand or more miles. It is not uncommon for some dark varnish deposits to be present on the rotors, but this cleans up readily with some liquid paraffin. The unit has its own external reservoir of gear oil, and provided this is monitored, units can survive a very long time. However, air filtration is critical because the close running tolerance of the rotors and blower housing will not tolerate the induction of sand or other contaminants. These will quickly score the rotor housing and damage the blower.
Gear wear on a properly maintained unit will be negligible, the SKF bearings will outlast most motors, and the part most susceptible to wear is easily replaced. This part would be the front seal, behind the drive pulley, which eventually will wear a bright spot into the pulley shaft and then begin to leak. Replacing this seal does require removal of the belt and pulley, but the part is available at most better transmission supply houses for less than $10.
This is a standard volumex unit after rebuilding. I ran a full case polish on this one. Time consuming, but comes out nicely due to the high quality of the aluminum castings. Seals and rear bearings are easy to source. Front bearings are more difficult to come by. This unit only had 30K, front bearings were still good.I sold this one to Tom McGafffigan in Califonia once I found one of the larger volumetrico blowers.
ABARTH SUPERCHARGER:
Although the ABARTH units share the same basic design concept as the volumex blowers, there are several key differences in terms of configuration. The most notable is the location of the rotor drive gears which transfer power from the directly driven rotor to the slave rotor, while maintaining an accurate 90 degree phase difference between the rotor shafts. On the volumetrico unit, these phasing gears are located in the front housing, directly behind the front cover plate. On the ABARTH units, this is reversed, with the drive gears occupying the rear housing. The volumetrico units have small vacuum take-off pipes near the bearing races to evacuate mixture from the blower once the engine is turned off. The ABARTH units omit this feature. The external oil reservoir is also omitted, as the units are fed with engine oil. As noted earlier, the FIAT 131 units contain a twin-gear scavenge pump in the tail housing.
From left to right: ABARTH 131 blower viewed from front of unit, from induction side, rear oil pump with end cover removed, gears of oil pump. The gear with the keyed shaft fits into a slot in the tail end of the lower rotor shaft.
ABARTH R10 DISASSEMBLY PROCEDURE:
This is the method I use, not necessarily the one endorsed by FIAT or ABARTH. If you have a better way, go for it. If you are scratching your head trying to figure out how you are going to get the rotor nuts off after you remove one and then have no way of holding onto the rotors, then read the below carefully. If the front end nut of the upper rotor releases first, you can set about making a holding fixture (or contact me about using mine). If the phasing nut lets go first, follow the instructions below, then re-set the rotors at 90 degrees and make your holding fixture, either way you will want one for reassembly.

1) Clean, degrease and drain oil from unit overnight. Tilting the unit upwards at the nose will help to drain.
2) Remove nuts, washers, and front cover from unit. Be careful not to damage the thin, brittle fiber gasket beneath.
3) Remove rear cover from unit, exposing synchronizing gears. Carefully remove the fiber gasket.
4) Inside of rear cover shows keyed shaft of driven oil pump gear. Hole to the left feeds oil pump.

5) Note direction of gear skew. Also note that lower rotor has slot for oil pump drive.
6) You will need two large breaker bars with 36mm sockets. Apply to opposite ends of upper rotor and s-q-u-e-e-z-e to remove nut.
7) If the gear end nut comes off first, don't worry. Simply gently rotate both rotors so you can see down between them.
8) With the rotors parallel, a 3/4" wood block can be inserted to safely hold the rotors while you remove the other nuts.

9) Flat side of nuts face inwards, but there's no chamfer on threads so check closely for burrs.
10) Perhaps we'll never know why only one gear has a vestigal keyway- but so does the R10 blower's drive pulley.
11) A firm tap with a rubber mallet breaks the factory silicone sealant and releases blower housing.
12) CAREFULLY slide blowers from housing. Then the rotors can be removed from end bearings.

13) A strategically placed zip tie will keep the bearings from falling apart and allow handling of the end plates.
14) Inside, the bearing races are recessed from the plate surface. There's a matching step in each rotor to close the gap.
15) You can then secure the other bearings the same way, then tap free the remaining endplate from the inside gently with your mallet handle.
16) Watch these little o-rings (near thumb and forefinger). They don't always stay in the grooves in the housing, as you can see here.

17) Now you can do bearing replacement or check oil pump gears as necessary- refer to earlier pictures of gear configuration.
18) The blower part number is inside the rear housing- note the "R10" designation.
MAKING A HOLDING FIXTURE:
There is one tricky part to rebuilding one of these blowers, and that is the fact that the rotors must be aligned at exactly ninety degrees to one another. Because of the significant torque of the fasteners, this is a bit harder than it looks. The factory obviously used some kind of fixture for this, perhaps some kind of plate with plugs that fit into the hollow ends of the rotor shafts? Since I had nothing to use as an example, I figured the best way to do this was to make a fixture that surrounded both rotors. Casting solder in place seemed like a good way to do this, as the solder is soft enough so as not to harm the rotors.