A key question in nuclear RNA surveillance is how target RNAs are recognized. To address this, we identified in vivo binding sites for nuclear RNA surveillance factors, Nrd1, Nab3 and the Trf4/5–Air1/2–Mtr4 polyadenylation (TRAMP) complex poly(A) polymerase Trf4, by UV crosslinking. Hit clusters were reproducibly found over known binding sites on small nucleolar RNAs (snoRNAs), pre‐mRNAs and cryptic, unstable non‐protein‐coding RNAs (ncRNAs) (‘CUTs’), along with ∼642 predicted long anti‐sense ncRNAs (asRNAs), ∼178 intergenic ncRNAs and, surprisingly, ∼1384 mRNAs. Five putative asRNAs tested were confirmed to exist and were stabilized by loss of Nrd1, Nab3 or Trf4. Mapping of micro‐deletions and substitutions allowed clear definition of preferred, in vivo Nab3 and Nrd1 binding sites. Nrd1 and Nab3 were believed to be Pol II specific but, unexpectedly, bound many oligoadenylated Pol III transcripts, predominately pre‐tRNAs. Depletion of Nrd1 or Nab3 stabilized tested Pol III transcripts and their oligoadenylation was dependent on Nrd1–Nab3 and TRAMP. Surveillance targets were enriched for non‐encoded A‐rich tails. These were generally very short (1–5 nt), potentially explaining why adenylation destabilizes these RNAs while stabilizing mRNAs with long poly(A) tails. The exosome and Trf4/5–Air1/2–Mtr4 polyadenylation (TRAMP) complexes together with the Nrd1–Nab3 RNA‐binding heterodimer have an important role in RNA surveillance. Here, the global analysis of Nrd1, Nab3 and Trf4 binding sites identifies targets for the nuclear surveillance system, including mRNAs, ncRNAs and RNA polymerase III transcripts.