  We raise a conjecture that asymptotics for Chebyshev polynomials in a complex
domain can be given in terms of the reproducing kernels of a suitable Hilbert
space of analytic functions in this domain. It is based on two classical
results due to Garabedian and Widom. To support this conjecture we study
asymptotics for Ahlfors extremal polynomials in the complement to a system of
intervals on $\mathbb R$, arcs on $\mathbb T$, and its continuous counterpart.
