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The typical rating of a hot wire relay contacts is 35 amp
A #3 copper wire with an insulation rating of 75 or 90 degrees C is rated at 100 and 110 amps consecutively.
A #4 copper conductor with an insulation factor of 75 or 90 degrees C is rated at 85 amps.
You never, ever mix wire sizes within a circuit. However you can wire a 30 amp circuit using AWG # 8/3 wire, although that is overkill and AWG #10 wire is what you would normally use on a 30 amp circuit.
Yes, the wire size has to be increased. The existing 100 amp service will now probably have a #3 conductor with an insulation factor of 75 or 90 degrees C which is rated for 100 and 105 amps respectively. Increasing to a 150 amp service will use a #1/0 wire size. If you are thinking of an upgrade, skip the 150 amp service and go to a 200 amp panel. New homes are installing 200 amp 42 circuit panels. The extra cost is only reflected in the materials as the labour costs will be the same regardless whether a 150 amp or a 200 amp panel is installed. The wire size for a 200 amp panel is #3/0. With an insulation factor of 75 or 90 degrees C the rating is 200 or 210 amps respectively.