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You would just need to go into the “add action” section for the Grow form and specify what you want to happen inside ConvertKit when someone joins through that form.
You most likely would want to add a tag to the subscriber that you would then add as a trigger for the automation you want to send them into.
You don’t need to do anything to specifically add them to a broadcast, since usually you just send those out in real time to everyone on your list.
However, in my personal opinion, I don’t think the Grow forms are GDPR compliant since they force the user to consent to receiving emails when they sign up through the form. So for me personally, I would only use their form for a newsletter opt-in, since by opting into your newsletter, the person is clearly consenting to receive emails from you anyway.