how about reading the Unclos?
both (b) the International Court of Justice and (c) an arbitral tribunal are resided in the Peace Palace in Hague. the PCA is authorized by the United Nations. no matter if the court is the owner of a certain building or a renter.
Article 287
Choice of procedure
1. When signing, ratifying or acceding to this Convention or at any time thereafter, a State shall be free to choose, by means of a written declaration, one or more of the following means for the settlement of disputes concerning the interpretation or application of this Convention:
(a) the International Tribunal for the Law of the Sea established in accordance with Annex VI;
(b) the International Court of Justice;
(c) an arbitral tribunal constituted in accordance with Annex VII;
(d) a special arbitral tribunal constituted in accordance with Annex VIII for one or more of the categories of disputes specified therein.