Gordo, if I can find the picture, I'll show you a stud buck that swam the Ohio from Blennerhassett Island to 618 down along the river in Belpre. It tried to jump a brick and wrought iron fence after the swim and got snagged. It was a good 150" deer. I also know of a buck that was shot along the river and attempted to swim to Musthapha Island while gut shot. Deer are excellent swimmers. I doubt they do it unless they have to, but a 45' swim across a river won't completely deter them if they want to be on the other side.
As for me, when I was doing a ton of summer road scouting a few years ago and saw a buck in velvet in the summer, then during the rut in November that was 5 miles from A to B. The holler he was running allowed him to access a huge area while searching for does and food. In all likelihood, his home range could have been several square miles.
On the flip side of the coin is Captain Jack. I honestly believe his home range is contained in 300 acres. My general opinion is most mature bucks stay within a square mile or two with a few times of the year being the exception. And like most experts say, I agree that home range shrinks over time.