First, of the Greek world, we have the Catalogue of Women (sometimes called the Ehoiai). This is a debatable entry, as it lacks a strict narrative. Instead, it's the account of the birth of heroes traced through their mothers. I mention it because there is a close relationship between ancient Greek genealogical poetry and Greek narrative ...
There's a nice little book by Malcolm Davies (St John's College, Oxford) titled "The Greek Epic Cycle", which deals exactly with what you are asking for. Here's the table of contents of the edition I have:
The Epic Cycle
The Little Iliad
The Sack of Troy
The Returns ...
Martin West's Loeb volume Greek Epic Fragments collects all the available fragments for the Titanomachy and a short introduction (2 paragraphs) on it. This is also where you'll find all the available fragments for early Greek epic.