The processes that regulate star formation within molecular clouds are still not well understood. Various star formation scaling relations have been proposed as an explanation, one of which is to formulate a relation between the star formation rate surface density {Sigma}SFR and the underlying gas surface density {Sigma}gas. In this work, we test various star formation scaling relations, such as the Kennicutt-Schmidt relation, the volumetric star formation relation, the orbital time model, the crossing time model and the multi free-fall time-scale model, towards the North American Nebula and Pelican Nebula and in the cold clumps associated with them. Measuring stellar mass from young stellar objects and gaseous mass from CO measurements, we estimate the mean {Sigma}SFR, the star formation rate per free-fall time and the star formation efficiency for clumps to be 1.5M_{sun}/yr/kpc^2^, 0.009 and 2.0 per cent, respectively, while for the whole region covered by both nebulae (which we call the 'NAN' complex) the values are 0.6M{sun}/yr/kpc^2^, 0.0003 and 1.6 per cent, respectively. For the clumps, we notice that the observed properties are in line with the correlation obtained between {Sigma}_SFR and {Sigma}gas, and between {Sigma}SFR and {Sigma}gas per free-fall time and orbital time for Galactic clouds. At the same time, we do not observe any correlation with {Sigma}gas per crossing time and multi free-fall time. Even though we see correlations in the former cases, however, all models agree with each other within a factor of 0.5dex. It is not possible to discriminate between these models because of the current uncertainties in the input observables. We also test the variation of {Sigma}SFR with the dense gas but, because of low statistics, a weak correlation is seen in our analysis.

Cone search capability for table J/MNRAS/500/3123/table2 (Physical parameters of the cold clumps associated with the NAN complex)

Cone search capability for table J/MNRAS/500/3123/table4 (Physical parameters of the clumps associated with dense regions)

Cone search capability for table J/MNRAS/500/3123/tablea1 (List of all the 3038 YSOs associated with NAN complex)