The concept of planar hypercoordinate (e.g., penta- and hexacoordinate) carbons is intriguing [Exner, K; Schleyer, P. v. R. Science 2000, 290, 1937] as it is neither compatible with the standard rule of three-dimensional chemical bonding nor with the maximum tetracoordination. Herein we undertake a comprehensive study of the planar tetra- (ptC), penta- (ppC), and hexacoordinate carbon (phC) by covering the whole family of carbon-boron mixed clusters Cm=1-4Bn=4-8 and their anions. The potential energy surface of every carbon-boron cluster is sampled by using the basin-hopping global search algorithm coupled with ab initio geometry optimization. A large number of planar tetra-, penta-, and hexacoordinate carbon (local-minimum) structures are obtained. Several structures such as the phC consisting of C2B5, C2B5-, etc. are reported for the first time. In particular, a ptC corresponding to the global minimum of CB4 is revealed, which appears to be highly stable for future synthesis. The boron-centered isomers are generally the more stable structures for planar multicoordinate carbons (ptC, ppC, and phC). The planar tetra-, penta-, and hexacoordinate boron are the prevalent structural motifs in low-lying isomers of the carbon-boron clusters. However, stability of the ptC and ppC units can be reinforced over the boron-centered isomers by attaching proper hydrocarbon unit -(CH)(n)- to form the so-called "hyparenes" [Wang, Z. X.; Schleyer, P. v. R. Science 2001, 292, 2465]). A new hyparene molecule is suggested for future synthesis of novel planar hypercoordinate carbon compounds.