This is from About.com
"Many young men, and even some older ones who haven’t found the right people to ask, are curious about morning erections. Most men have the experience, with some regularity, of waking up in the morning with an erection.
What Is A Morning Erection?
Morning erections, colloquially referred to as "morning wood" and scientifically defined as nocturnal penile tumescence (NPT) are a healthy and normal physiological response that most men experience. Morning erections would be better described as the tail end of a series of nighttime erections, as they are just the last erection in a series.
On average a healthy male will have between three and five erections in a full night sleep, with each erection lasting between 25 -35 minutes.
Causes of Morning Erections
It is a common myth that morning erections are caused by a full bladder. This is untrue. While the reason for morning erections is unknown, we do know that the erections are closely associated with REM sleep (the time in the night when you dream and brain activity changes). These erections are also associated with an increase in heart rate. It isn’t known for sure if the erections are a result of the other physiological changes, more research is required. Some suggest that morning erections are a way for your body to make sure everything is in working order. "
I guess I am pretty average... If I wake up in the middle of the night, most of the time I am hard as a rock... in the morning... 99% of the time - HARD!