We present the results from an X-ray spectral analysis of active galactic nuclei (AGN) in the Chandra Deep Field-South, AEGIS-XD and Chandra-COSMOS surveys, focussing on the identification and characterisation of the most heavily obscured, Compton thick (CT, N H > 10 24 cm −2 ) sources. Our sample is comprised of 3184 X-ray selected extragalactic sources, which has a high rate of redshift completeness ( 97.6%), and includes improved photometric redshifts over previous studies. We use spectral models designed for heavily obscured AGN which self consistently include all major spectral signatures of heavy absorption. We identify CT sources not selected through our spectral fitting method using X-ray colours, validate our spectral fitting method through simulations, and take considerations for the constraints on N H given the low count nature of many of our sources. After these considerations we identify a total of 100 CT AGN with best-fit N H > 10 24 cm −2 and N H constrained to be above 10cm −2 at 90% confidence. These sources cover an intrinsic 2-10 keV X-ray luminosity range of 10 42 − 3 × 10 45 erg s −1 and a redshift range of z=0.1-4. This sample will enable characterisation of these heavily obscured AGN across cosmic time and to ascertain their cosmological significance. These survey fields are sites of extensive multi-wavelength coverage, including near-infrared CANDELS data and far-infrared Herschel data, enabling forthcoming investigations into the host properties of CT AGN. Furthermore, by using the torus models to test different covering factor scenarios, and by investigating the inclusion of the soft scattered emission, we find evidence that the covering factor of the obscuring material decreases with L X for all redshifts, consistent with the receding torus model, and that this factor increases with redshift, consistent with an increase in the obscured fraction towards higher redshifts. The strong relationship between the parameters of obscuration and L X points towards an origin intrinsic to the AGN, however the increase of the covering factor with redshift may point towards contributions to the obscuration by the host galaxy. We make N H , Γ (with uncertainties), observed X-ray fluxes and intrinsic 2-10 keV luminosities for all sources analysed in this work publicly available in an online catalogue.