  The transition temperature ($T_c$) of QCD is determined by Symanzik improved
gauge and stout-link improved staggered fermionic lattice simulations. We use
physical masses both for the light quarks ($m_{ud}$) and for the strange quark
($m_s$). Four sets of lattice spacings ($N_t$=4,6,8 and 10) were used to carry
out a continuum extrapolation. It turned out that only $N_t$=6,8 and 10 can be
used for a controlled extrapolation, $N_t$=4 is out of the scaling region.
Since the QCD transition is a non-singular cross-over there is no unique $T_c$.
Thus, different observables lead to different numerical $T_c$ values even in
the continuum and thermodynamic limit. The peak of the renormalized chiral
susceptibility predicts $T_c$=151(3)(3) MeV, wheres $T_c$-s based on the
strange quark number susceptibility and Polyakov loops result in 24(4) MeV and
25(4) MeV larger values, respectively. Another consequence of the cross-over is
the non-vanishing width of the peaks even in the thermodynamic limit, which we
also determine. These numbers are attempted to be the full result for the
$T$$\neq$0 transition, though other lattice fermion formulations (e.g. Wilson)
are needed to cross-check them.
