The rule of thumb for what determined any given trait, from summaries of the relevant science in the early 2000s, was "genetics 50%, unique environment 40-50%, shared environment 0-10% [heavily weighted toward the 0% end of things]".
Of course that division of influence (1) varies by the particular trait; and (2) is itself dependent on environmental conditions; when the general background is extremely impoverished, shared environmental influences may matter in a way that they don't when the background is lush.
Steven Pinker writing in The Blank Slate pounded on the message that it is essentially impossible for parents to have any predictable non-genetic influence on their children, but that there was still plenty left to be determined after the genes had their say. He recommended greater acceptance of the concept of fate.