  Ideal Sharvin contact in a multimode regime shows the conductance
$G\approx{}G_{\rm Sharvin}=g_0k_F{}W/\pi$ (with $g_0$ the conductance quantum,
$k_F$ the Fermi momentum, and $W$ the contact width) accompanied by strongly
suppressed shot-noise quantified by small Fano factor $F\approx{}0$. For
ballistic graphene away from the charge-neutrality point the sub-Sharvin
transport occurs, characterised by suppressed conductance
$G\approx{}(\pi/4)\,G_{\rm Sharvin}$ and enhanced shot noise $F\approx{}1/8$.
All these results can be derived from a basic model of quantum scattering,
involving assumptions of infinite height and perfectly rectangular shape of the
potential barrier in the sample. Here we have carried out the numerical
analysis of the scattering on a family of smooth barriers of finite height
interpolating between parabollic and rectangular shapes. We find that tuning
the barrier shape one can modify the asymmetry between electron- and hole-doped
systems. For electronic dopings, the system crosses from Sharvin to sub-Sharvin
transport regime (indicated by both the conductance and the Fano factor) as the
potential becomes closer to the rectangular shape. In contrast, for hole
dopings, the conductivity is strongly suppressed when the barrier is parabolic
and slowly converges to $G\approx{}(\pi/4)\,G_{\rm Sharvin}$ as the potential
evolves towards rectangular shape. In such a case the Sharvin transport regime
is inaccessible, shot noise is generically enhanced (with much slower
convergence to $F\approx{}1/8$) comparing to the electron-doped case, and
aperiodic oscillations of both $G$ and $F$ are prominent due to the formation
of quasibound states.
