If you want to identify the fungus, I don't think that the picture is enough. You can also isolate the DNA and amplify and sequence the ITS region and Blast against the gene bank and you will get an accurate answer. I hope this answer could help
It absolutely belongs to the group of Ascomycetes (what else can it be?). However, to identify the fungus at the family and genus level by optical microscopy is impossible.
Perhaps if you could provide photographs with a lesser amount of material would help to better visualize the micelium and determine the way of hyphae growth and spore formation.
If it's important to you to identify the fungus at the genus and/or the species level, I recommend you to follow the comments that our collegeagues have previously provided.
Many anamorph genera produce conidia with branched arms like the ones in your picture, e.g. Diplocladiella, Tripospermum, Actinocladium, etc.
There excellent books with illustrations and descriptions which could be helpful to identify this fungus, such as Ellis' "Dematiaceous Hyphomycetes" and "More Dematiaceous Hyphomycetes" and Seifert et al.'s "The Genera of Hyphomycetes"
I think that you fungus belongs to anamorphic genus Tripospermum and it is very close to Tripospermum myrti (Lind) S.J. Hughes(Order Capnodiales, Family Capnodiaceae, Class Dothideomycetes, Phylum Ascomycota), but not to Meliola.