The 'SNL' alum was at The Grove shopping plaza in L.A. Saturday with 6-year-old Saint West, who was holding on tight to Papa Pete while they perused the shops and right before they went into the Cheesecake Factory ... with what appears to be a lone bodyguard standing by.

Eyewitnesses tell us that hat Saint's wearing is actually one PD bought for him ... which the kid seemed to appreciate, seeing how he let Pete guide him through the paved Grove paths.

We're told there was no sight of Kim here, or the other children. And no -- Ye wasn't around either ... as you could imagine. He'd probably flip his lid if he saw this with his own two 👀.

Unfortunately for him, he might just have to get used to it ... because it's becoming clearer the longer this relationship lasts that Pete has certainly met the children already, and will continue to be around. Not just that, but he's pretty cozy with them ... and they with him.

We already saw North sitting in Pete's lap a few months ago while he was driving her around in a golf cart ... which is the sort of thing that, y'know, actual fathers do usually.

Of course, there's also the issue of the apparent neck tattoo he got that bears all the children's first name initials (plus Kim's) ... which caused a lot of controversy in and of itself.

It would appear Kim's all good with it though ... and again, it just speaks to how serious they are as a couple. It's been less than a year that they've been together -- and yet, they're almost looking like a blended family these days. Especially with moments like these.

Something tells us that if Pete and Kim are still together through the holidays, this year's Kardashian Christmas card is going to potentially look very different via a new addition.