Be honest first about how much of Typeform you are actually using. If the conversational, one-question-at-a-time flow is central to your completion rates, the closest matches are Typebot, which builds conversational flows on a canvas, and HeyForm, whose builder does conversational forms with custom themes and logic; most of the other builders render standard multi-field forms instead. If what you really need is reliable data collection for surveys, intake, or research, the open tools are on much stronger ground. LimeSurvey is a mature survey platform with 30-plus question types, skip logic, and branching, while TDuck gives you a drag-and-drop builder with conditional display and submission limits by IP or device.
Weigh where the product boundary moves once you self-host. Typeform bundles the editor, hosting, spam control, and email delivery into one service; run your own and those become your responsibilities. For a public marketing form that matters a lot, so test spam handling, deliverability, and behavior under a traffic spike after a campaign launches. For internal or field collection it matters far less. KoboToolbox exists precisely because humanitarian and research teams need dependable data capture on infrastructure they control, and it exposes a REST API for pulling results out.
The submitted responses are the easy part to move, since Typeform exports them to CSV and offers an API. The form itself, including question wording, logic jumps, hidden fields, endings, and embeds, almost always has to be rebuilt by hand. Plan a mapping document, test the old and new forms side by side, then update embeds and shared links before you retire the original.