Sambar deer were introduced, by the Acclimatisation Society, to Victoria, Australia around 1860. They are free range and totally wild, Generally located in various State Forests and National Parks. They have completely adapted to the Australian environment. According to the Game Management Authority data, some 118,900 deer were harvested by hunters in 2021. That should give you an idea of the health of the population. I'm cynical enough to believe that most of the talk about the sambar "problem" is from the antis who have discovered that sambar are highly valued by hunters.
Rusa deer were also introduced, but have not been as successful, although some research suggests they interbred with sambar and have become part of the sambar population.
Fallow deer were a farming fad in the late 2oth century. Like most fads, it crashed and burned. Many farmers just opened the gates and let them disappear. There are now significant wild populations, but not at the numbers of the sambar.
Free range Hog deer can be found along the south eastern coast of Victoria. Hunting is controlled by season and a tag system. While the populations in mush of the Hog Deer's natural range are either extinct or endangered, the Victorian population is healthy and expanding. They are one of the few wild Hog Deer populations in the world that can be hunted.