In this thesis we study the spatial distribution of extremely luminous high-redshift dust-enshrouded star-forming submillimetre galaxies (SMGs) towards the environments of 16 powerful high-redshift radio galaxies and a quasar (AGN) using continuum observations at 1.1 mm taken with the AzTEC camera. This AGN sample represents a subset of the ongoing AzTEC Cluster Environment Survey (ACES). We target powerful high-redshift AGN, using them as signposts of protoclusters, since under the ΛCDM scenario these early structures are formed in the highest density regions of the Universe. The number of ACES targets and the increased area covered by each AzTEC map of our protocluster sample allows us to examine the surface density (number counts) of SMGs towards these regions with greater significance than previous studies. We estimate the integrated number counts for the fields of individual ACES targets, but in the majority of cases the density of sources with S1.1mm > 4 mJy falls within the 95% confidence interval of the density of sources in a comparison sample of unbiased blank fields. Only in the surroundings of 4C+23.56, PKS1138-262 and MRC0355-037 do we detect individual overdensity signals of ∼ 2 with a significance of ∼ 3δ. When we perform a stacking analysis on the complete sample of AzTEC maps, we also find an overdensity of ∼ 2, with greater statistical significance, covering an area of 3-arcmin diameter centred on the AGN (corresponding to a co-moving diameter of 1.7-7.5 Mpc over the redshift range 0.5 < z < 6.3 of the sample). This is in good agreement with the analysis of previous studies. In addition, the large size of our maps allows us to establish that beyond a radius of 1.5 arcmin, the radial surface density of SMGs falls very quickly to reach a typical value for a blank field distribution of SMGs. The measured angular extent of this overdensity is in agreement with estimates of the virial radii of local clusters.