Question

Why BF3 forms an adduct(chemical formed by just addition) with ammonia?

Answer 1

NH3 is an electron-rich species with a lone pair on Nitrogen atom and so is always ready to co-ordinate this lone pair to other species.
While, BH3 is an electron-deficient species with an incomplete octet of Boron(B). So BH3 is always looking for species which can donate electrons to it and complete the octet of Boron(B).

So clearly, NH3 and BH3 get together, NH3 co-ordinates its lone pair to the empty p-shell of Boron forming a co-ordinate bond to give rise to an adduct.