"To meet"?

[zeme]

What are the differences between kohtuma, täitma, and vastama?
Are there other words for "to meet"? (to establish contact between two people or things)

[Midian]

Simple version (I'm sure ainurakne will come around and give better answer soon )

Kohtuma - Just like you wrote. To establish contact between two people or things.

Täitma:
Täida ämber veega. Fill a bucket with water.
Unistusi täitma/täide viima. To fulfill dreams.

Vastama:
Vastan küsimusele. (I am) answering a question.
Vastab nõuetele. Meets the requirements.

[ainurakne]

Simple version (I'm sure ainurakne will come around and give better answer soon )

Actually, there's not much more to add, you said pretty much it all.

One synonym to kohtuma is also 'kokku saama' (literally: to get together), but no other way to say it comes to my mind right now.

vastama can be also translated as 'to respond'.

More examples for täitma:
'oma kohust täitma' - to do one's duty, to meet one's obligation, to fulfill one's duty.
'instruktsioone täitma' - to execute instructions (in computing).
'käsku täitma' - to follow an order, to do what one is told to do.