It's all in new court docs, obtained by TMZ Sports, in which Kane says his estranged wife, Anna Kane, has been lying to him about her pregnancy since July.

The San Jose Sharks star claims up until earlier this month, he had believed Anna was pregnant with their second child, which was due in February 2022.

Evander says Anna had spoken about the baby often, and he says he had seen her belly grow with his own eyes throughout the last several weeks.

Evander, though, says after he reviewed recent medical bills -- it was brought to his attention that Anna had actually had an abortion way back in July.

Evander is accusing Anna of pretending to be pregnant for months ... going as far as wearing "some sort of pregnancy belly" to deceive him and cause him mental trauma.

Evander says all of it is so deeply disturbing, he's worried about the potential impact it might have on the couple's daughter -- and he's now requesting the court step in and give him full custody of their girl while also ordering Anna to undergo an examination to prove she's mentally stable.

For her part, Anna said in her own court docs that she did have the abortion in July, and acknowledged "I was less than forthcoming with [Evander] with regards to my decision."

She admitted in the docs that she "did not inform [Evander] or the court that I was no longer pregnant." She did deny, however, wearing any sort of prosthetics in an attempt to look pregnant.

Anna also claimed in her docs she is mentally stable and is fully capable of caring for the couple's daughter -- and is asking the court to deny Evander's requests.

Evander has been granted temporary custody of the child -- with a hearing on the matter slated for December.