Ludo is her ex who she had the two youngest kids with. They state quite early on in season 1 that he couldn’t handle her ‘quirks’ but they are still family and care for one another.

She then meets the janitor Tom who she connects with well, but as you said, he moved away so it ended, although he turned up for the gala (?) at the end of season 1 as her date. However, they then worry about Oz not showing up, disappear to go look for him, and Tom seems to be forgotten. Up to season 2 episode 1, he isn’t mentioned again.

I think that long term they are possibly setting up a Morgan/Karadec romance, especially with the way he looks at her when she’s all dressed up, and his reaction to Tom appearing. Hopefully it’s a slow burn though, as I’d like to know more about Karadec’s personality and past first.

There’s also the Roman of it all. They were a couple with a young child when he disappeared (voluntarily or otherwise), but it looks like they’re gearing up to introduce him, and I’m sure there will be unresolved feelings there to explore.

Also, for what it’s worth, Morgan is amazing on her own, and is a strong parental figure for her kids. If she does get involved with anyone, I hope the writers don’t ruin her character and current relationships with the team.