I know DNA Polymerase synthesizes new strand DNA on the basis of the template strand, the same for RNA polymerase. But is there really an enzyme which could join nucleotides together by covalent bond from 5-3 or 3-5?
Polynucleotide phosphorylase synthesizes RNA from ribonucleoside diphosphates. For example, it will make polyA from ADP. No template is required and any rNDP will work.