Paying your TurboTax fees does not submit and transmit your tax return. You would have selected File in the left menu, and followed the instructions until you selected the Transmit my returns now button.
You must select that button to electronically send your return to the government.
Once you've done that, the next thing you should see is a Transmission Successful screen. This means your return is on its way to the government agency.
How do I e-file my personal (individual) tax return?
Please check your e-file status here -How do I check my e-file status? to see if your return was submitted. When you e-file your federal return you will receive two emails from TurboTax. The first one states that your return was submitted. The second email will tell you if your federal return was accepted or rejected. If you e-filed a state return, there will be a third email to tell you if the state accepted or rejected your state or rejected your state return.
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If you find that you did not submit your return, you can follow the instructions in the TurboTax FAQ below, to complete e-filing your return or the link I provided above to e-file: