You'll only see that kind of vignetting in two cases:
If you're using a circular fisheye, where the lens is designed to have an image circle small enough to fall completely inside the frame borders.
You're using a lens that was designed for a smaller format on a larger one (i.e., most typically, an APS-C ultrawide zoom lens on a full-frame sensor).
Because you haven't given us enough specifics, we don't know how the lens maps, which lens design or formats we're talking about, so in this case, no, there is no "generic parameter" to go by to tell you what the magic focal length is where there's no vignetting any more. It depends, and will have to be ascertained by trial and error.
For example, we know that the Tokina 11-17/2.8 DX fisheye lens tends to begin vignetting on full frame around 15mm, but has more of a weird butterfly-shaped image area, because a ton of people have had to try it and report back on their success to the interwebz (including Ken Rockwell). Meanwhile, the Sigma 12-24 that's designed for full-frame—has no vignetting even down to 12mm.
The Canon EF 8-15 f/4L IS USM is a unique lens in that it's designed for full frame, and intended to be a circular fisheye at 8mm, but a full frame one at 15mm. And we know that the vignetting mostly disappears at 14mm from reviews.
On a crop, of course, the use of a circular fisheye designed for full-frame changes. But then there is the Sigma 4.5mm circular fisheye for crop that exhibits the full image circle within the frame, rather than just dark corners as the full-frame Sigma 8mm does on crop, as your two example images show.