  We present a study of the deconfinement phase transition of one-flavour QCD,
using the multiboson algorithm. The mass of the Wilson fermions relevant for
this study is moderately large and the non-hermitian multiboson method is a
superior simulation algorithm. Finite size scaling is studied on lattices of
size $8^3\times 4$, $12^3\times 4$ and $16^3\times 4$. The behaviours of the
peak of the Polyakov loop susceptibility, the deconfinement ratio and the
distribution of the norm of the Polyakov loop are all characteristic of a
first-order phase transition for heavy quarks. As the quark mass decreases, the
first-order transition gets weaker and turns into a crossover. To investigate
finite size scaling on larger spatial lattices we use an effective action in
the same universality class as QCD. This effective action is constructed by
replacing the fermionic determinant with the Polyakov loop identified as the
most relevant Z(3) symmetry breaking term. Higher-order effects are
incorporated in an effective Z(3)-breaking field, $h$, which couples to the
Polyakov loop. Finite size scaling determines the value of $h$ where the first
order transition ends. Our analysis at the end - point, $h_{ep}$, indicates
that the effective model and thus QCD is consistent with the universality class
of the three dimensional Ising model.
  Matching the field strength at the end point, $h_{ep}$, to the $\kappa$
values used in the dynamical quark simulations we estimate the end point,
$\kappa_{ep}$, of the first-order phase transition. We find $\kappa_{ep}\sim
0.08 $ which corresponds to a quark mass of about 1.4 GeV .
