Galaxies with the mass of the Milky Way dominate the stellar mass density of the Universe but it is uncertain how and when they were assembled .
Here we study progenitors of these galaxies out to z = 2.5 , using data from the 3D-HST and CANDELS Treasury surveys .
We find that galaxies with present-day stellar masses of \log ( M ) \approx 10.7 built \sim 90 % of their stellar mass since z = 2.5 , with most of the star formation occurring before z = 1 .
In marked contrast to the assembly history of massive elliptical galaxies , mass growth is not limited to large radii : the mass in the central 2 kpc of the galaxies increased by a factor of 3.2 ^ { +0.8 } _ { -0.7 } between z = 2.5 and z = 1 .
We therefore rule out simple models in which bulges were fully assembled at high redshift and disks gradually formed around them .
Instead , bulges ( and black holes ) likely formed in lockstep with disks , through bar instabilities , migration , or other processes .
We find that after z = 1 the growth in the central regions gradually stopped and the disk continued to build , consistent with recent studies of the gas distributions in z \sim 1 galaxies and the properties of many spiral galaxies today .