They aren't domesticated, but they've made themselves at home. They are muscovy ducks. I'll see if I can get some photos. Thanks for the link to the state thread.
that’s illegal and they are not pets. also if you kill them or move them that is also illegal. just leave them alone
Since Muscovies are not really native to the U.S, there is some leniency as far as what you can do with them. For example, in the state of Florida, the Muscovy is actually considered a pest by many folks. Texas is a little different as the ducks are closer to their native range, but in most counties, they're not protected and can be killed/caught whatever.
From my understanding, the only counties in the state of Texas where they are protected are Hidalgo, Starr, or Zapata County. (Most of the counites being close to the Mexico border/near the duck's native region)
"(a) Control of muscovy ducks. Anywhere in the contiguous United States except in Hidalgo, Starr, and Zapata Counties in Texas, and in Alaska, Hawaii, and U.S. territories and possessions, landowners and Federal, State, Tribal, and local wildlife management agencies, and their tenants, employees, or agents may, without a Federal permit, remove or destroy muscovy ducks (Cairina moschata) (including hybrids of muscovy ducks), or their nests, or eggs at any time when found. Any authorized person may temporarily possess, transport, and dispose of muscovy ducks taken under this order"
“If the duck is not destroyed (killed), it must be transported to Hidalgo, Starr, or Zapata County. These three counties are the only counties in Texas and the United States where the .duck may not be destroyed and can be released.”
The laws might vary in your county, so it would be best to talk to your city council and ask what their rules are first.
Best of luck dealing with them.