I set the screen resolution to 1024 x 768 on Splashtop, so text appears larger.
Here is a photo of how my Mac screen appears in the Splashtop app on my iPhone X.you can see some black bars on either side because my iPhone X has a much wider screen resolution than on my iPad
Here is a screenshot of the Splashtop app and how it appears using the iPad app on my iPad 10.5. Note there are no black bars because the setting on my Mac screen is set to a resolution of 1024 x 768 on my Mac, which more closely mirrors the shape of my iPad screen (which is more square).
So to answer your question, the iPad app will fill your entire screen as long as the remote computer mirrors the shape of your iPad screen. If your remote computer is setup as a very “wide” screen (which is popular nowadays with wide screen monitors) then you will likely see black bars surrounding the image.
Hope that helps! You can also use Jump Desktop and “manually” change your remote display properties to something like 1024 x 768 to achieve the same result.