  We study the coorbital flow for embedded, low mass planets. We provide a
simple semi-analytic model for the corotation region, which is subsequently
compared to high resolution numerical simulations. The model is used to derive
an expression for the half-width of the horseshoe region, x_s, which in the
limit of zero softening is given by x_s/r_p = 1.68(q/h)^(1/2), where q is the
planet to central star mass ratio, h is the disc aspect ratio and r_p the
orbital radius. This is in very good agreement with the same quantity measured
from simulations. This result is used to show that horseshoe drag is about an
order of magnitude larger than the linear corotation torque in the zero
softening limit. Thus the horseshoe drag, the sign of which depends on the
gradient of specific vorticity, is important for estimates of the total torque
acting on the planet. We further show that phenomena, such as the Lindblad
wakes, with a radial separation from corotation of ~ a pressure scale height H
can affect x_s, even though for low-mass planets x_s << H. The effect is to
distort streamlines and to reduce x_s through the action of a back pressure.
This effect is reduced for smaller gravitational softening parameters and
planets of higher mass, for which x_s becomes comparable to H.
