We use a sample built on the SDSS DR7 catalogue and the bulge-disc decomposition of Simard et al. (2011) to study how the bulge and disc components contribute to the parent galaxys star formation activity, by determining its position in the star formation rate (SFR) - stellar mass (M$_{star}$) plane at 0.02$<z<$0.1. We use the bulge and disc colours as proxy for their SFRs. We study the mean galaxy bulge-total mass ratio (B/T) as a function of the residual from the MS ($Delta_{MS}$) and find that the B/T-$Delta_{MS}$ relation exhibits a parabola-like shape with the peak of the MS corresponding to the lowest B/Ts at any stellar mass. The lower and upper envelop of the MS are populated by galaxies with similar B/T, velocity dispersion and concentration ($R_{90}/R_{50}$) values. Bulges above the MS are characterised by blue colours or, when red, by a high level of dust obscuration, thus indicating that in both cases they are actively star forming. When on the MS or below it, bulges are mostly red and dead. At stellar masses above $10^{10.5} $M$_{odot}$, bulges on the MS or in the green valley tend to be significantly redder than their counterparts in the quiescence region, despite similar levels of dust obscuration. The disc color anti-correlates at any mass with the distance from the MS, getting redder when approaching the MS lower envelope and the quiescence region. We conclude that the position of a galaxy in the LogSFR-LogM$_{star}$ plane depends on the star formation activity of its components: above the MS both bulge and disk are actively star forming. The nuclear activity is the first to be suppressed, moving the galaxies on the MS. Once the disk stops forming stars as well, the galaxy moves below the MS and eventually to the quiescence region. This is confirmed by a large fraction ($sim45%$) of passive galaxies with a secure two component morphology.
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