You mean the fake midget whites? They may or may not exist depending on who you talk to. While they are supposed to have a broad breast, they can fly.. At least one person that I know of that got "Midget Whites" found that the ones he purchased did not meet the SOP requirements.
@Flashpoint supposedly has Midget Whites.
Fake Midget Whites or not - I wanted them as pet turkeys due to the inherent friendliness they exhibit.

My original four Narragansetts always wanted to be close, the hens would steal anything I laid down; however, they were NOT lap turkeys. They do not want to even be touched. Even though they were hand raised from a couple of days old - they are still to this day - merely lurkers.
As to flying, the MW hens do even as adults. The toms did in the beginning as young birds, but once they were adults they stopped. The hens often perch - not only on top fence bars, but the camper, the sheds, and the house. The good thing is (and with very few exceptions), they stay within my perimeter
3-foot tall chainlink fence. Their actual runs consist of 8-foot tall hardware cloth in most places (complete with aprons) and with a net on top. However, they also free-range when I am outside.
Currently, I have 14 MW's. My 3 oldest toms are always close to me and the older hens will sit in my lap or in a chair next to me. I also have 6 Blue Slates, 3 Bourbon Reds, 1 tiny (midget) red bronze, and 4 Narragansett (lost my 2 original hens). The only one who purposely flies over my pen fences that do not have nets, is a young Narragansett jake named TT - because he believes his place is to be with me at all times. Other than the MW's, he is the ONLY turkey over 6 months of age that is super friendly, although the midget red bronze may do the same (2 1/2 months).
Tom Collins
Digits and Mushroom (just sold Mushroom)