Hydrolase that deubiquitinates target proteins such as FOXO4; p53/TP53; MDM2; ERCC6; DNMT1; UHRF1; PTEN and DAXX. Together with DAXX; prevents MDM2 self-ubiquitination and enhances the E3 ligase activity of MDM2 towards p53/TP53; thereby promoting p53/TP53 ubiquitination and proteasomal degradation. Deubiquitinates p53/TP53 and MDM2 and strongly stabilizes p53/TP53 even in the presence of excess MDM2; and also induces p53/TP53- dependent cell growth repression and apoptosis. Deubiquitination of FOXO4 in presence of hydrogen peroxide is not dependent on p53/TP53 and inhibits FOXO4-induced transcriptional activity. In association with DAXX; is involved in the deubiquitination and translocation of PTEN from the nucleus to the cytoplasm; both processes that are counteracted by PML. Involved in cell proliferation during early embryonic development. Involved in transcription-coupled nucleotide excision repair (TC-NER) in response to UV damage: recruited to DNA damage sites following interaction with KIAA1530/UVSSA and promotes deubiquitination of ERCC6; preventing UV-induced degradation of ERCC6. Contributes to the overall stabilization and trans-activation capability of the herpesvirus 1 trans-acting transcriptional protein ICP0/VMW110 during HSV-1 infection. Involved in maintenance of DNA methylation via its interaction with UHRF1 and DNMT1: acts by mediating deubiquitination of UHRF1 and DNMT1; preventing their degradation and promoting DNA methylation by DNMT1. Exhibits a preference towards 'Lys-48'-linked ubiquitin chains. Increases regulatory T- cells (Treg) suppressive capacity by deubiquitinating and stabilizing the transcription factor FOXP3 which is crucial for Treg cell function (PubMed:23973222). {ECO:0000269|PubMed:11923872; ECO:0000269|PubMed:14506283; ECO:0000269|PubMed:15053880; ECO:0000269|PubMed:16160161; ECO:0000269|PubMed:16964248; ECO:0000269|PubMed:18590780; ECO:0000269|PubMed:18716620; ECO:0000269|PubMed:20153724; ECO:0000269|PubMed:21745816; ECO:0000269|PubMed:22411829; ECO:0000269|PubMed:22466611; ECO:0000269|PubMed:22466612; ECO:0000269|PubMed:22689415; ECO:0000269|PubMed:23973222}.