If a training program tells you to run say 5 miles one day, what are the consequences of splitting up that run? Is there some gray area where you can reap the same/most benefits (say splitting run to 4 and 1 VS. 5 one-milers)? Studies to show the difference would be great.
If you are marathon training and your run that day is 20 miles, the point is to get used to running that mileage so I would say splitting the run is detrimental to the training. I think there may be some leeway in the lower mileage zones though?
While I don't have any studies to confirm my ideas, common sense can go a long way:
If you need to travel to a suitable place to run, like a forest or a track, you don't want to do this more often than necessary as it wastes times.
Almost any exercise requires some time spent on warming up and/or cooling down. If you break up your exercise, you effectively double the time spent or wasted on this as well.
When you work out, several chemical responses occur, like the building up of endorphin, cortisol or adrenaline. These help regulate processes in the body such as increasing your blood pressure, stimulating your heart to beat faster or inhibit your indigestion. If you break up your workout, your body has to built up all these hormone levels again, before being able to work out at a sufficient level.
Working out at a sufficient intensity causes very small damage, which will impair it's capabilities. While your body will start to restore (and superimpose), it would be better to give the muscles sufficient rest to do so. Splitting up the work means you would potentially undo any recovery your muscles have undergone already.
Fatigued muscles are more prone to injuries. So if you've worked out hard during the first part of your exercise and your muscles are fatigued, there's an increased chance of injury, because the muscles are no longer able to withstand high loads.
If you work out hard enough to start sweating, you would either have to shower twice or endure your own smell during the day ;-)
It can depend on your type of workout, some workouts require you to built up some measure of endurance, so cutting up the workout is not an option.
It's often not advisable to eat (too much) right before working out, so splitting up your workouts can put some strain on your eating habits (unless you can workout all day long like celebrities).
However, there are off course practical reasons why not everyone is able to workout for long stretches of time. So if you're simply unable to do so, splitting up exercises (most often) won't hurt you either.
I couldn't find anything for splitting "short" runs. From the lack of discussion on the Internet, I infer that the running world is probably just telling me to suck it up, stop thinking about it, and just run. Safe to assume then that splitting short runs is fine, split any which way, and I can give myself full credit for "getting the miles in".
It seems that training runs for a 5K thru a half-marathon distance do not qualify as candidates for a "split run" according to this article which had a great table.