Q: Just put a new carburetor, battery, starter relay, alternator, car stalls out while driving and battery dies when restarted

The battery should be load tested. Simply charging the battery or measuring voltage is not adequate. Measure charging output, too. You want to confirm that the ignition system, including for instance the ignition coil and ignition switch, are not intermittently cutting out. Coils can fail as temperature rises (resistance increases with temperature) so if you run the car for a while and all of a sudden it quits, measure the resistance of the coil windings to see if that provides a clue. Apart from that, the ENTIRE primary side ignition circuit has to be checked, using voltage drop testing (and testing of the hall effect sensor in the distributor), to rule the primary side in or out. If you want the required diagnostic steps performed by a certified Mechanic, dispatched by YourMechanic right to your location, please request a stalling diagnostic and the responding certified mechanic will get this taken care of for you. If you have further questions or concerns, do not hesitate to re-contact YourMechanic as we are always here to help you.