The collapse transition of a single polymer chain in two and three dimensions was studied using the bond-fluctuation model. The obtained exponents v of the scaling law [S-N(2)]similar to N-2v agree with values proposed in the literature as well as above, at and below the Theta-temperature T-Theta. Transition curves and scaling analysis plots are presented. The scaling function alpha(S)(3) tau N-1/2 vs tau N-1/2 has a pronounced maximum before leveling off in the fully collapsed regime in accordance with the theory [alpha(S)(2)=[S-N(2)]/[S-N(2)](Theta), tau=(T-T-Theta)/T-Theta]. An analyzing of the subchain distances leads to disagreements with the blob model. The subchains are locally swollen for T>T-Theta and shrunken for T

Keywords:SELF-AVOIDING WALKS;TO-COIL TRANSITION;END DISTRIBUTION FUNCTION;THETA-POINT;2 DIMENSIONS;RENORMALIZATION-GROUP;QUANTITATIVE THEORY;DIFFERENT REGIMES;EXCLUDED-VOLUME;LINEAR-POLYMERS