No i did not mean family guy/simpsons/futurama; those are very well known and are serial cartoons
Euro (and i think there were some american as well) short animated movies (they ussually do not last more than 10 minutes) typically have dark themes. For example there are russian animated films of some russian short stories by famous authors, like Gogol's 'the overcoat'.
It was on ERT, the greek state channel(s), so i trust you would only have seen its logo during olympics (or eurovision

).
I was looking for a film titled "the village".
This was an award winning short animated movie, about two young people in a village of miserable and hostile older people. One of the older characters cared only about collecting gold and hiding it under his bed, then at night bringing it out so as to kiss it ceremonially.
Short animated film is not about serials, although there are some which have several different plots, using the same characters (or at least the same images of characters, since you rarely get too accustomed to one character).
An american such animated film had quite an underground tone, with ugly drawings and a background of bestiality for example..