Fallow have been introduced almost everywhere. The entirety of Europe, Argentina, Texas, Australia, NZ, South Africa. It’s probably slightly unclear where it’s original range ended but the introduced deer well outnumber what’s in Iran and Turkey. Axis deer are native to Indian subcontinent. From what I can think you can hunt them in Texas, Hawaii, Australia, Argentina probably a few more places. Sambar are native to SE Asia and India. I don’t know where all they’ve been introduced, not as widespread as other two. There are Rusa Stags too. New Caledonia and Mauritius are probably most famous place for hunting them, not sure where else they’ve been introduced. Red deer have been moved many places in world from Europe, NZ and Argentina most famous. Sika deer from Japan and other more northern parts of east Asia have been widely transplanted. Even white tail deer have been put in Norway. It’s a long list of all the deer that have been moved. The only unsuccessful deer outside it’s native range is European roe deer for whatever reason. There were even moose introduced to NZ at one time.