Hydrolase that deubiquitinates polyubiquitinated target proteins such as MDM2, MDM4 and CCND1 (PubMed:17290220, PubMed:19917254, PubMed:19838211). Isoform 1 and isoform 4 possess both ubiquitin-specific peptidase and isopeptidase activities (By similarity). Deubiquitinates MDM2 without reversing MDM2-mediated p53/TP53 ubiquitination and thus indirectly promotes p53/TP53 degradation and limits p53 activity (PubMed:17290220, PubMed:19838211). Has no deubiquitinase activity against p53/TP53 (PubMed:17290220). Prevents MDM2-mediated degradation of MDM4 (PubMed:17290220). Plays a role in the G1/S cell-cycle progression in normal and cancer cells (PubMed:19917254). Regulates the circadian clock by modulating its intrinsic circadian rhythm and its capacity to respond to external cues (By similarity). Associates with clock proteins and deubiquitinates core clock component PER1 but does not affect its overall stability (By similarity). Regulates the nucleocytoplasmic shuttling and nuclear retention of PER1 and its repressive role on the clock transcription factors CLOCK and ARNTL/BMAL1 (By similarity). Plays a role in the regulation of myogenic differentiation of embryonic muscle cells (By similarity). Circadian clock output effector that regulates Ca(2+) absorption in the small intestine. Probably functions by regulating protein levels of the membrane scaffold protein NHERF4 in a rhythmic manner, and is therefore likely to control Ca(2+) membrane permeability mediated by the Ca(2+) channel TRPV6 in the intestine. Thiol-dependent hydrolysis of ester, thioester, amide, peptide and isopeptide bonds formed by the C-terminal Gly of ubiquitin (a 76-residue protein attached to proteins as an intracellular targeting signal). Cleavage is inhibited by ubiquitin in a dosage-dependent manner. Cleavage is blocked by ubiquitin aldehyde. Homooligomer (By similarity). Found in trimeric complex with MDM2 and MDM4 and USP2. Interacts with CCND1; the interaction is direct and promotes its stabilization by antagonizing ubiquitin-dependent degradation. Interacts (via N-terminus and C-terminus) with MDM2. Interacts with MDM4. Interacts with PER1 (By similarity). Interacts with KCNQ1; counteracts the NEDD4L-specific down-regulation of I(Ks) and restore plasma membrane localization of KCNQ1 (PubMed:22024150). Isoform 4: Interacts with PDZD3 and CLTC (By similarity). Localizes in the spermatid head in late-elongating spermatids in the thin area between the outer acrosomal membrane and the plasma membrane. Predominantly expressed at membranes. Expressed in mesangial cells of the kidney and in different types of glomerulonephritides (at protein level). Down-regulated by cisplatin (at protein level). The different N-terminus extensions of isoform 1 and isoform 4 determine their respective subcellular localization and differentiel effect on myoblast fusion and accumulation of muscle-specific proteins. The different N-terminus extensions of isoform 1 and isoform 4 are not essential for their catalytic activity. Belongs to the peptidase C19 family. USP2 subfamily.