  Based on a tight-binding model and a recursive Green's function technique,
spin-depentent ballistic transport through tinny graphene sheets (flakes) is
studied. The main interest is focussed on: electrical conductivity, giant
magnetoresistance (GMR) and shot noise. It is shown that when graphene flakes
are sandwiched between two ferromagnetic electrodes, the resulting GMR
coefficient may be quite significant. This statement holds true both for zigzag
and armchair chiralities, as well as for different aspect (width/length)
ratios. Remarkably, in absolute values the GMR of the armchair-edge graphene
flakes is systematically greater than that corresponding to the zigzag-edge
graphene flakes. This finding is attributed to the different degree of
conduction channel mixing for the two chiralities in question. It is also shown
that for big aspect ratio flakes, 3-dimensional end-contacted leads, very much
like invasive contacts, result in non-universal behavior of both conductivity
and Fano factor.
