The RNA exosome is fundamental for the degradation of RNA in eukaryotic nuclei. Substrate targeting is facilitated by its co-factor Mtr4p/hMTR4, which links to RNA-binding protein adaptors. One example is the trimeric human nuclear exosome targeting (NEXT) complex, which is composed of hMTR4, the Zn-finger protein ZCCHC8, and the RNA-binding factor RBM7. NEXT primarily targets early and unprocessed transcripts, which demands a rationale for how the nuclear exosome recognizes processed RNAs. Here, we describe the poly(A) tail exosome targeting (PAXT) connection, which comprises the ZFC3H1 Zn-knuckle protein as a central link between hMTR4 and the nuclear poly(A)-binding protein PABPN1. Individual depletion of ZFC3H1 and PABPN1 results in the accumulation of common transcripts that are generally both longer and more extensively polyadenylated than NEXT substrates. Importantly, ZFC3H1/PABPN1 and ZCCHC8/RBM7 contact hMTR4 in a mutually exclusive manner, revealing that the exosome targets nuclear transcripts of different maturation status by substituting its hMTR4-associating adaptors.