Question

After the collapse of a nebular cloud, atoms begin gravitating together to form a condensed center. What happens next in the star formation process?

Answer 1

Well, first of all, I don't think "After the collapse of a nebular cloud ..."
is the first time that "atoms begin gravitating together".  Seems to me like
that's what was going on all the time, and it's what caused the nebular cloud
to collapse in the first place.

In any case, once the pressure and temperature at the center get high enough,
you get "ignition" of nuclear fusion, and that's when you first have a "star". 

Answer 2

Answer:

The core of the star is ignited.

Explanation:

Through the acummulation of mass caused by gravitation, the protostar becomes heavier and heavier until the pressure in its center, the core, is enough to initiate thermonuclear reactions. This reactions will be the source of the energy of the star during its entire life, as long as it shines.

The amount of mass needed for the protostar to ignite its core is known as stellar mass.