Accepts ubiquitin from the E1 complex and catalyzes its covalent attachment to other proteins. In vitro catalyzes 'Lys-48'-linked polyubiquitination. Cooperates with the E2 UBCH5C and the SCF(FBXW11) E3 ligase complex for the polyubiquitination of NFKBIA leading to its subsequent proteasomal degradation. Performs ubiquitin chain elongation building ubiquitin chains from the UBE2D3-primed NFKBIA-linked ubiquitin. UBE2D3 acts as an initiator E2, priming the phosphorylated NFKBIA target at positions 'Lys-21' and/or 'Lys-22' with a monoubiquitin. Cooperates with the SCF(SKP2) E3 ligase complex to regulate cell proliferation through ubiquitination and degradation of MYBL2 and KIP1. Involved in ubiquitin conjugation and degradation of CREM isoform ICERIIgamma and ATF15 resulting in abrogation of ICERIIgamma- and ATF5-mediated repression of cAMP-induced transcription during both meiotic and mitotic cell cycles. Involved in the regulation of the cell cycle G2/M phase through its targeting of the WEE1 kinase for ubiquitination and degradation. Also involved in the degradation of beta-catenin. S-ubiquitinyl-[E1 ubiquitin-activating enzyme]-L-cysteine + [E2 ubiquitin-conjugating enzyme]-L-cysteine = [E1 ubiquitin-activating enzyme]-L-cysteine + S-ubiquitinyl-[E2 ubiquitin-conjugating enzyme]-L-cysteine. S-ubiquitinyl-[E1 ubiquitin-activating enzyme]-L-cysteine + [acceptor protein]-L-lysine = [E1 ubiquitin-activating enzyme]-L-cysteine + N(6)-monoubiquitinyl-[acceptor protein]-L-lysine. CDC34-catalyzed polyubiquitin chain assembly activity is stimulated by the conjugation of NEDD8 to the CUL1 SCF E3 ligase complex subunit. Protein modification; protein ubiquitination. Interacts with SCF (SKP1-CUL1-F-box protein) E3 ubiquitin ligase complex. Identified in a SCF (SKP1-CUL1-F-box protein) E3 ubiquitin ligase complex together with HINT1 and RBX1. When cullin is neddylated, the interaction between the E2 and the SCF complex is strengthened (By similarity). When phosphorylated, interacts with beta-TrCP (BTRC) (By similarity). Interacts with casein kinase subunit CSNK2B. Interacts with CNTD1; this interaction regulates the cell-cycle progression (PubMed:32640224). The phosphorylation of the C-terminal tail plays an important role in mediating nuclear localization. Colocalizes with beta-tubulin on mitotic spindles in anaphase. The C-terminal acidic tail is required for nuclear localization and is involved in the binding to SCF E3 ligase complexes, and more specifically with the CUL1 subunit. Phosphorylated by CK2. Phosphorylation of the C-terminal tail by CK2 controles the nuclear localization. Belongs to the ubiquitin-conjugating enzyme family.