I saw a documentary in which a mother T-Rex smuggled aboard a freighter to rescue its baby which had been kidnapped to LA. It wreaked all kind of havoc, but once re-united with its young, it waddled off peacefully into the credits. 
When I Googled it, the plural was Reges.
If we are considering it to be a word fully adopted into English, rather than Latin, then surely it would be rexes.
There’s no particular correlation between the size of the theropod and the degree of reduction of the arms. Carnotaurus of South America had arms that were even more reduced than Tyrannosaurus, (Carnotaurus on left)but it wasn’t nearly as big. (In this case, the arm bones are much more reduced than in tyrannosaurs, and may have been non-functional. This is an instance in which the arms may in fact be vestigial.)
Spinosaurus on the other hand was possibly the largest theropod of all, but as you say had well developed arms.
But why were they so much smaller than the arms of most other theropods? That’s the question.
Don’t crocodiles carry their hatchlings in their jaws? Seems that lots of big sharp teeth don’t necessarily get in the way of carrying babies.
It made Merriam-Webster’s main entries, so I’d say that qualifies.
ETA: One thing to consider about the tiny arms is that it is thought that the “hands” could not rotate downward, that they pretty much always faced each other. (IIRC)
From some other Doper, a long time ago in a similar thread:
**To throw them up in the air,
And wave them like he just don’t care!**
Going green by not searching. 
“Much smaller” is a relative term. Theropods tend to have all small arms. Some had a straighter posture than others, meaning that a Spinosaurus probably used his arms to run four-legged, will T-Rex’es were pretty much just bipedal.
It would have been impossible for Spinosaurus to have “run four-legged”; the arms are much too small for that, and are not articulated in such a way to make quadrupedal locomotion feasible for any distance. T. rex was not just “pretty much” bipedal; it was obligately bipedal.
T. rex’s arms are proportionally smaller than those of most other theropods, making the question of why they were like that of some interest. Just saying that all theropods had small arms doesn’t contribute anything to the discussion.
Hah! 
Has anyone examined the tendon and muscle indentations left on the bones? I’m just wondering if the typical range and direction of movement had been determined.
Also, maybe there were flaps, like wings, attached to the abdomen and the lower part of the arms. Not to fly, but to spread open the flap in a display of mating courtship the way that some ground dwelling birds do with their wings. This is also why I ask about the examination of the bones as the possibility of a flap might be apparent.
Augh… edit did not take…
Any ways, there is a WikiPedia section for the arms. They are in fact very limited in their capability but I also think the neck can be folded over and down so the mouth and arms could meet.
As for the OP question… I think they were small as they did not need to be any bigger. The legs are well developed as are the jaws. There was a lot of muscle attacked to these two which dictates that how it got it’s prey: a high-speed attack with a grappling bite to the body of the prey. The arms were probably folded-in out of harms-way. Those short, powerful, jaws probably crushed the prey to death. Once the prey was dead, the arms presumably held the carcass in place either on the ground or maybe a smaller chunk close to the chest while T-rex ripped pieces from it.
True enough. Still, the small arms of a Spinosaurus could be used to crouch or rest using them, much like an ape does.
And I honestly don’t see a particularly unusual difference in proportional size between the Rex and other large theropods such as the Gigantosaurus. Pointing out what looks to me like a flawed premise is a fairly good contribution to the discussion, I think.
T-Rex was almost horizontal when he ran, right? So the arms would have further reach than you’d think if he were always upright.
Could they be used to protect the neck and chest from fighting prey?
yes, because let’s face it, his arms were the scariest part of his anatomy 
Or applauding the play at golf matches!
I always thought it was to hold its cigarettes: http://1.bp.blogspot.com/_WQbgYtjne58/So4fheIXsYI/AAAAAAAAAPw/SZAuu-Sw8g0/s400/extinct.jpg
Could we look to the kangaroo for an answer to this, or is that just ridiculous? I mean, the 'roo has relatively small upper limbs combined with a long, powerful tail and larger powerful legs. Roos commonly use their upper limbs for balancing while grazing in a quadrupedal way, and also during high-speed locomotion.
(I’m not saying that T-Rexes bounced their way along, mind. But perhaps their upper limbs were just long enough to use in a similar way.)
Not sure whether 'roo upper limbs are proportionally longer than T-Rexes, though.
Would you be willing to arm wrestle with a T-Rex? I didn’t think so.
T. Rex forelimbs seem to be proportionally smaller than kangaroos, and unable to reach the ground unless the beast is lying on it’s belly. The are also very small in proportion to all the every other part of their body. The hands also have an unusual two claw form. Fossil bones indicate the arms were heavy and well muscled, so not useless if they could reach something.
But the mystery is also one of expectations. Someone examining modern mammal fossils might wonder why humans had such a small tail. As mentioned previously in the thread, a variety of dinosaurs had proportionally small forelimbs, something that would be expected in animals with T form bipedalism. Somewhere along the line, T. Rex ancestors may have simply developed progressively larger legs, heads, and tails, while never developing large forelimbs because there was no benefit from them. And possibly there was a benefit from having them proportionally smaller, but we may never find enough evidence to determine what that benefit was.
They are.