For me, the use of zheng zai is sb+ zheng zai + v.

e.g. wo zheng zai du shu= I am reading. But you may also say wo zai du shu. “zheng” can be omitted.

However, if you say the book is on the desk= shu zai zhuo zi shang. In this circumstance, you can not say shu zheng zai zhuo zi shang. It does not make sense.

Therefore, usually the use of zai is “sth+ zai+n.”