Hi Rather amused by these exchanges. I am a Tarboton - note the single T!!!!
I assume that at some point these families were linked - our line comes from Thorner, Leeds. It would be great to work out when the name morphed. The single T version seemed to die out in England in the 1880s - at least in the Thorner area. the name survives in plenty in South Africa (following immigration there in 1850) and clearly those descendants are now migrating all over the place and even back to England!