  Growth of carbon substituted magnesium diboride Mg(B1-xCx)2 single crystals
with 0<x<0.15 is reported and the structural, transport, and magnetization data
are presented. The superconducting transition temperature decreases
monotonically with increasing carbon content in the full investigated range of
substitution. By adjusting the nominal composition, Tc of substituted crystals
can be tuned in a wide temperature range between 10 and 39 K. Simultaneous
introduction of disorder by carbon substitution and significant increase of the
upper critical field Hc2 is observed. Comparing with the non-substituted
compound, Hc2 at 15K for x=0.05 is enhanced by more then a factor of 2 for H
oriented both perpendicular and parallel to the ab-plane. This enhancement is
accompanied by a reduction of the Hc2-anisotropy coefficient gamma from 4.5
(for non-substituted compound) to 3.4 and 2.8 for the crystals with x = 0.05
and 0.095, respectively. At temperatures below 10 K, the single crystal with
larger carbon content shows Hc2 (defined at zero resistance) higher than 7 and
24 T for H oriented perpendicular and parallel to the ab-plane, respectively.
Observed increase of Hc2 cannot be explained by the change in the coherence
length due to disorder-induced decrease of the mean free path only.
