The collection does not contain any unpublished marvels. All Ptolemaic texts are published and all the literary ones too. A fourth volume of P.Haun. is half-finished and will appear, one day.
Papyri in the collection have occasionally shown affiliations with other collections mostly, one would suppose, through the hazards of the papyrus market. Thus the Sappho, which has already been mentioned was bought at about the same time as Achille Vogliano was bying in Egypt. But also P.Haun 14+15 which were discovered by P.J. Sijpesteijn to belong with P.Mich. 679, see AB-J and Vincent McCarren "P. Haun. 14, P. Mich. 679 and P. Haun. 15. - A Re-edition", ZPE 58, 1985, pp. 71-79.
An as yet unpublished fragment (inv. 319) of a codex-leaf is the other half of the leaf published as P.Bon. 1 (somebody is working on it and it will be published).
Some papyri from the Hauniensis collection have also been published outside the series:
inv. 400 was published by M.W. Haslam as P.Turner 8
inv. 21 AB-J as P.Turner 25
inv. 326c by I. Andorlini in Greek Medical Papyri I. Firenze 2001. No 11, pp. 119-129
inv. 25 by AB-J in Papyri in honorem Johannis Bingen octogenarii (P.Bingen) ed. Henri Melaerts (Studia varia Bruxellensia ad orbem Graeco-Latinum pertinentia V), Leuven, 2000. 241-243. = P.Bingen 58.
inv. 182. i A.J.B. Sirks & K.A. Worp Papyri in Memory of P.J. Sijpesteijn.( = American studies in papyrology 40) 2007, pp. 77-78. = P.Sijp. 14.
The three published volumes are:
Papyri graecae haunienses, fasciculus primus. Literarische Texte und Ptolemäische Urkunden. Herausgegeben von Tage Larsen. Copenhagen 1942.
Papyri graecae haunienses, fasciculus secundus. Letters and mummy labels from Roman Egypt edited with translation and commentary by Adam Bülow-Jacobsen. Bonn 1981 (= PTA Band 29)
Papyri graecae haunienses, fasciculus tertius. Subliterary texts and Byzantine documents from Egypt edited with translation and commentary by Tage Larsen (deceased) and Adam Bülow-Jacobsen. Bonn 1985 (= PTA Band 36)