Are the electrons in a coordinate covalent bond donated by both the bonded atoms?

In a coordinate covalent bond, the electrons are conceived to be supplied by the ONE atom............

Consider the acid-base behaviour of ammonia:

##H_3N(aq) + H_2O(l) rightleftharpoons NH_4^(+) + HO^-##

The lone pair on ammonia is conceived to donate electrons to form a coordinate covalent bond with the proton. Of course in ammonium ion, ##NH_4^+##, all of the ##N-H## bonds are equivalent, but nitrogen has a formal positive charge because its lone pair has been donated to ##H^+##.