I had a very large ovarian cyst (I have a looped bowel due to previous bodged surgery for something else and it had grown through it so they didn't see it all on the scan) mine was 10 cm x 9 x 7 (I think it was in 2009 and so much has happened since I can't remember exactly but it was huge cause they never measured it all). Mine did not go after pregnancy. I had problems in the pregnancy BUT was told that it was NOT due to the cyst. My consultants plan was to leave it unless it caused problems to bubs and operate after.
I had to have mine taken out by op - they got 1 1/2 liters PLUS of fluid from in, they thought from what they saw it was old and had been there a long time. I had it taken out by key hole surgery - even with the additional problems with my bowel the surgery was sucessful and the recovery was AMAZING (compared to myc section). The recovery time was brilliant - I couldn't believe how much so.
So if anyone has a large one that does not go away and does need surgery - please don't panic, from my experience it was a very simple op (and I am a huge chicken - hate GA and hospitals!!!).
BUT most cysts do go away and as said about they are functional and very common.