All have both common and unique features of genomic DNA and virion structure. It remains uncertain whether the similarities of different families of this grouping of NCLDV are due to independent recruitment of the same or related host genes during viral replication or if they simply share a common viral ancestor, although the latter is under heavy scrutiny and controversy 
It is probable that these viruses evolved before the separation of eukaryotes into the extant crown groups. The ancestral genome was complex with at least 41 genes, including: (1) the replication machinery; (2) up to four RNA polymerase subunits; (3) at least three transcription factors; (4) capping and polyadenylation enzymes; (5) the DNA packaging apparatus; (6) structural components of an icosahedral capsid and the viral membrane.
^Lakshminarayan M. Iyer, L. Aravind, and Eugene V. Koonin. "Common Origin of Four Diverse Families of Large Eukaryotic DNA Viruses." Journal of Virology, December 2001, p. 11720-11734, Vol. 75, No. 23. Link.