  (Abridged) Studies have shown that a Jovian mass planet embedded in a viscous
protoplanetary disc (PPD) can accrete gas efficiently through the gap and
doubles its mass in $\sim 0.1$ Myr. The planet also migrates inwards on a
timescale of $\sim 0.1$ Myr. These timescales are short compared to PPD
lifetimes, and raise questions about the origins of cold giant exoplanets.
However, PPDs are unlikely to be globally turbulent, and instead they may
launch magnetised winds such that accretion towards the star occurs in laminar
accretion flows located in narrow layers near the surfaces of the disc. The aim
of this study is to examine the rate at which gas accretes onto Jovian mass
planets that are embedded in layered PPDs. We use 3D hydrodynamical simulations
of planets embedded in PPDs, in which a constant radial mass flux towards the
star of ${\dot m} = 10^{-8}$ M$_{\odot}$ yr$^{-1}$ is sustained. We consider a
classical viscous alpha model, and also models in which an external torque is
applied in narrow surface layers to mimic the effects of a magnetised wind. The
accreting layers are parameterised by their column densities $\Sigma_{\rm A}$,
and we consider values in the range 0.1 to 10 g cm$^{-2}$. The viscous model
gives results in agreement with previous studies. We find the accretion rate
onto the planet in the layered models crucially depends on the planet's ability
to block the wind-induced mass flow. For $\Sigma_{\rm A}=10$ g cm$^{-2}$, the
planet torque can block the mass flow through the disc, accretion onto the
planet is slow, and a mass doubling time of 10 Myr is obtained. For
$\Sigma_{\rm A}=0.1$ g cm$^{-2}$, accretion is fast and the mass doubling time
is 0.2 Myr. Although the radial mass flow through the layered disc models is
always $10^{-8}$ M$_{\odot}$ yr$^{-1}$, adopting different values of
$\Sigma_{\rm A}$ leads to very different gas accretion rates onto gas giant
planets.
