According to a study by the Society for Endocrinology, it could actually be that as certain parts of the brain shut down during REM sleep, his brain is no longer keeping his penis in check. Whereas normally the brain is regulating the penis and making sure erections only occur when needed, during REM the penis is free to do whatever it wants. And what it wants to do is get hard.
http://www.cosmopolitan.com/sex-lov...boyfriend-always-waking-up-with-morning-wood/
You... just used cosmopolitan as a source?
Good YouTube video.morning wood repairs and maintains functionality