Kris -- who was required to sit for the depo by Kim's legal team -- insisted he only knew Myla for a few months, even though we're told they [have been involved] since January.

Sources connected with Kris tell us ... he admitted he spoke "generally" to Myla about Kim, but only when she asked questions, such as ..."What's she like in real life?" Kris testified he never spoke to Myla about his divorce.

And our sources say ... Kris was asked various questions about his allegation that Kim defrauded him into marrying her and her motivation was just a crass ploy for ratings. We're told Kris offered no specifics ... no evidence of fraud.