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It took Tesla 3 weeks to get the information to me that I needed to have to apply for a title. I went to the Clerk, and then it took another 7 days for me to get the Title from the DMV. You mileage may vary.
In CA the title is sent to you directly. It usually takes 3-4 weeks, but covid has reduced their workforce. It may take longer. Once the paperwork is submitted to DMV, there is nothing Tesla can do to expedite.