Symmetric diblock copolymers in dilute solution were examined by means of Monte Carlo simulations on a cubic lattice with respect to chain-and block dimensions, shape, local structure and number of contacts. The solvent was either a common good one, a common 0-solvent or a selective one for the two blocks. In all cases, repulsive interactions are operative between the blocks. In addition, the underlying homopolymers (athermal and 0) were divided into two parts (and treated as a block copolymer) for comparison. Chain-length was varied from 40 to 1280 segments leading to the expected values for the critical exponent 2v = 1.2 for good solvent quality and 2v = 1.0 for 0-solvent. Copolymers in a selective solvent scale with an intermediate exponent, 2v = 1.13. The deviation of the mean squared dimensions of the copolymers from the sum of those of two homopolymers of the same length and for the same solvent quality as the blocks is largest for block copolymers in a common @-solvent (where it exceeds 20%), while the blocks themselves have mostly the same dimensions as their underlying homopolymers of equal length. The shape of the copolymers, expressed by the parameter 6 (asphericity) becomes more rod-like with increasing chain-length if there are (compact) 0-blocks in the molecule which are subject to mutual repulsive interaction. In these cases, 6 exceeds the value of the homopolymers in the limit of infinite chain-length. The number of contacts per segment approaches a limiting value with increasing chain-length which is ~0 . 2 0 for athermal chains and athermal blocks. For 0-chains and &blocks, a limiting value is not yet reached within the range of chainlengths investigated. The number of contacts per segment between two different blocks quickly tends to zero with increasing chain-length.