You've not said, but I presume you're asking about a mobile phone and when you block an individual number. The answer is that the blocking acts as a unconditional divert-all to call, and reject to text messages. Calls will divert unconditionally to voicemail (or elsewhere, if you configure your diverts accordingly), texts will simply not deliver.
Printing texts - depends what the motivation is. If it's purely your interest, then you'd best be looking at phone backup software, and seeing what functionality there may be to read the contents. EE as a network operator wouldn't offer anything here.
If there is criminal activity alleged, that's different - and you should report that to the Police. Legal authorities have their own processes, if just blocking the offending user doesn't achieve the necessary aims.
