Abstract: A pitch based carbon fiber, having a thermal conductivity in the direction of the fiber axis of from 500 to 1,500 W/m.multidot.K, a tensile modulus of at least 85 ton/mm.sup.2, a compression strength of at least 35 kg/mm.sup.2, a laminated layer thickness, Lc, of graphite crystallites of from 30 to 50 nm, and a ratio thereto of a spread, La, of graphite crystallites in the direction of the layer plane, of at least 1.5, has high thermal conductivity, excellent compression strength and an excellent tensile modulus of elasticity. When a cross section of said fiber in the direction of the fiber axis is observed by a polarization microscope with 1,000 X magnifications, the domain size as observed is at most 500 nm.

Abstract: A pitch-type carbon fiber made from a pitch having 1 a glass transition temperature width of at most 40.degree. C. as measured by a differential scanning calorimeter, 2 a proportion of the optically anisotropic phase of at least 10% by volume, and 3 a quinoline-insoluble content of at most 5% by weight, as a spinning raw material pitch.

Abstract: A pitch-type carbon fiber made from a pitch having 1 a glass transition temperature width of at most 40.degree.C. as measured by a differential scanning calorimeter, 2 a proportion of the optically anisotropic phase of at least 10% by volume, and 3 a quinoline-insoluble content of at most 5% by weight, as a spinning raw material pitch.

Abstract: Spinning pitch for carbon fibers, which (1) has a glass transition temperature width of at most 60.degree. C. as measured by a differential scanning calorimeter, (2) contains at least 80% by volume an optically anisotropic phase, and (3) shows a shear viscosity of 200 poise at a temperature of from 270.degree. to 370.degree. C.