How to display the Thank you message on our web page itself?

is it possible to NOT take people away from our website with the thank you message once a form has been submitted?

So have the thank you message ON our website - not on JotForm

I am not sure if I understand your query correctly. Do you mean to display the thank you page on your web site after submitting the form? Please note that if the form is embedded on any your web pages, the thank you page will be displayed on your web page itself. Please let us know the web page where the form is embedded or the URL that you are trying to access so that we can take a look and assist you further.

We will wait for your response. Thank you! 

thanks for your help - I have now done it - no problems - I have also signed up for a bronze account - paid my money and my shiny new form is working perfectly :-)

but I do have one more question - why do I get TWO copies of each message delivered to my inbox?

You have two notifications created for this form and it has almost the similar content. You can delete one which trigger only one email after the form submission.

When you are into a form builder, Click on Settings, go to Emails and delete one of the notifications.

Here is the article that gives more information on email notification - Setting-up-Email-Notifications