We present deep optical photometry from the DECam imager on the 4 m Blanco telescope of over 12 deg2 around the Carina dwarf spheroidal, with complete coverage out to 1 deg and partial coverage extending out to 2.6 deg. Using a Poisson-based matched-filter analysis to identify stars from each of the three main stellar populations, old, intermediate, and young, we confirm the previously identified radial age gradient, distance, tidal radius, stellar radial profiles, relative stellar population sizes, ellipticity, and position angle. We find an angular offset between the three main elliptical populations of Carina, and find only tentative evidence for tidal debris, suggesting that past tidal interactions could not have significantly influenced the Carina dwarf. We detect stars in the vicinity of, but distinct to, the Carina dwarf, and measure their distance to be 46±2 kpc. We determine this population to be part of the halo of the Large Magellanic Cloud at an angular radius of over 20 deg. Due to overlap in colour-magnitude space with Magellanic stars, previously detected tidal features in the old population of Carina are likely weaker than previously thought.