Terminal nucleotidyltransferase that catalyzes preferentially the transfert of ATP and GTP on RNA 3' poly(A) tail creating a heterogeneous 3' poly(A) tail leading to mRNAs stabilization by protecting mRNAs from active deadenylation (By similarity). Also functions as a catalytic subunit of a TRAMP-like complex which has a poly(A) RNA polymerase activity and is involved in a post-transcriptional quality control mechanism. Polyadenylation with short oligo(A) tails is required for the degradative activity of the exosome on several of its nuclear RNA substrates. Has no terminal uridylyltransferase activity, and does not play a role in replication-dependent histone mRNA degradation via uridylation (By similarity). ATP + RNA(n) = diphosphate + RNA(n)-3'-adenine ribonucleotide Component of a nuclear TRAMP-like complex, an ATP-dependent exosome regulatory complex consisting of a helicase (MTREX), an oligadenylate polymerase (TENT4B or TENT4A), and a substrate specific RNA-binding factor (ZCCHC7 or ZCCHC8). Several TRAMP-like complexes exist with specific compositions and are associated with nuclear, or nucleolar RNA exosomes. Excluded from nucleolus, weak staining detected in the cytoplasm. Belongs to the DNA polymerase type-B-like family. Was originally thought to have DNA polymerase activity.