Critical editions of purāṇas known to me are here listed by date of publication:

The Vāmana Purāṇa, critically edited by Anand Swarup Gupta. Varanasi: All-India Kashiraj Trust, 1967.

The Kūrma Purāṇa, critically edited by Anand Swarup Gupta. Varanasi: All-India Kashiraj Trust, 1971.

The Varāha Purāṇa, critically edited by Anand Swarup Gupta, 2 volumes. Varanasi: All-India Kashiraj Trust, 1981.

The Bhāgavata [Śrīmad Bhāgavata Mahāpurāṇa]: Critical Edition, edited by H. G. Shastri, Bharati K. Shelat, and K. K. Shastree, 4 volumes in 6 parts. Ahmedabad: B. J. Institute of Learning and Research, 1996 (1-3), 1999 (4-6), 1998 (7-9), 1997 (10), 1998 (11-12), 2002 (Epilogue).

The Critical Edition of the Viṣṇupurāṇam, edited by M. M. Pathak, 2 volumes. Vadodara: Oriental Institute, 1997, 1999.

The Critical Edition of the Mārkaṇḍeyapurāṇam, edited by M. L. Wadekar, 2 volumes. Vadodara: Oriental Institute, 2011 (volume 1 is chapters 1-75; volume 2 is chapters 76-88, the Devīmāhātmyam).

The Skandapurāṇa, vol. I, adhyāyas 1-25, edited by Rob Adriaensen, Hans T. Bakker, and Harunaga Isaacson, 1998; vol. IIa, adhyāyas 26-31.14, ed. by Hans T. Bakker and Harunaga Isaacson, 2005; vol. IIb, adhyāyas 31-52, ed. by Hans T. Bakker, Peter C. Bisschop, and Yuko Yokochi, 2014; vol. III, adhyāyas 34.1-61, 53-69, ed. by Yuko Yokochi, 2013. Supplement to the Groningen Oriental Studies, Groningen: Egbert Forsten, and Leiden: Brill. [This listing is not up to date; I think more volumes have been published in the last six years.]

A critical edition of the Vāyu-purāṇa is underway at the Oriental Institute, Vadodara.

The Ānandāśrama editions used multiple manuscripts. These include the Padma (1894), Brahma (1895), Agni (1900), Vāyu (1905), and Matsya (1907) purāṇas.

Of the Bibliotheca Indica editions, at least the Vāyu edited by Rajendralala Mitra (2 volumes, 1880, 1888) used multiple manuscripts.

A composite edition of the Bhāgavata-purāna with three or four commentaries is Śrīmad Bhāgavata Mahāpurāṇam, edited by P. Radhakrishna Sarma, and N. C. V. Narasimhacharya, 12 volumes (in 14 parts?). Tirupati: Tirumala Tirupati Devasthanams, 1989-2005 (not yet completed?).

A composite edition of the Brahma-purāṇa is found in Sanskrit Indices and Text of the Brahmapurāṇa, by Peter Schreiner and Renate Söhnen. Purāṇa Research Publications, Tübingen, 1. Wiesbaden: Otto Harrassowitz, 1987.

According to the extensive researches of R. C. Hazra, most of the purāṇas now extant are not the original ones. This is based on his gathering quotations from the purāṇas found in the old smṛti-nibandhas, and on descriptions of the contents of the purāṇas given in some of the purāṇas. The results of his researches were published in a series of journal articles, and mostly included in his book, Studies in the Purāṇic Records on Hindu Rites and Customs. He concluded that only seven of the now extant mahā-purāṇas can legitimately claim to be the original ones: Mārkaṇḍeya, Vāyu, Brahmāṇḍa, Viṣṇu, Matsya, Bhāgavata, and Kūrma, and even the Kūrma with considerable qualifications. Of the other eleven erstwhile mahā-purāṇas, he discovered the original Agni-purāṇa in manuscripts under the name Vahni-purāṇa. This was edited and published after his lifetime:

Vahni-Purāṇam, also referred to as Āgneya-Purāṇam, edited by Anasuya Bhowmik. Bibliotheca Indica Series, no. 336. Kolkata: The Asiatic Society, 2012 (includes as an Introduction the extensive 2-part article by Rajendra Chandra Hazra titled, “Studies in the Genuine Āgneya-Purāṇa alias Vahni-Purāṇa,” originally published in 1953 and 1954).

David Reigle

Colorado, U.S.A.