  We explore the initial conditions that lead to detached binary evolution of
massive pre-MS binaries and ask how large a fraction of the observed binary
systems may have been initially formed as low-mass protobinaries and later
undergone a significant accretion phase while remaining detached. We develop a
family of analytic models to describe the orbital separation, $a$, and mass
ratio, $q$, evolution. For a given mass accretion rate onto the binary system,
we define a recipe for distributing this mass between the two components. For
this we introduce a parameter $\eta$, such that
$\frac{\dot{M}_2}{\dot{M}_1}=q^\eta$ at any time, to determine the binary mass
ratio evolution. Depending on the choice of $\eta$, any type of mass ratio
evolution is possible. Furthermore, we use MESA, a detailed stellar structure
code, to calculate an extensive grid of binary sequences where a protobinary
undergoes accretion, and we identify the initial conditions that separates
detached from non-detached pre-MS binary evolution. A value of $\eta$ around 2
allows accretion growth in detached systems to form close massive binaries on
the Zero Age Main-Sequence with minimum orbital periods down to about 1.2 days
for $M_{\rm 1, ZAMS}=20-30M_{\odot}$ twin-binaries. $\eta=2$ can also reproduce
the observed population of binary systems with primary stars above
$6M_{\odot}$. The whole observed range of massive close binaries can form via
accretion growth in detached systems, making the binary formation channel of
accretion growth a strong contender to explain the formation of massive close
binaries, including progenitors of coalescing binary black holes.
