We use EAGLE to quantify the effect galaxy mergers have on the stellar specific angular momentum of galaxies, $j_{rm stars}$. We split mergers into: dry (gas-poor)/wet (gas-rich), major/minor, and different spin alignments and orbital parameters. Wet (dry) mergers have an average neutral gas-to-stellar mass ratio of $1.1$ ($0.02$), while major (minor) mergers are those with stellar mass ratios $ge 0.3$ ($0.1-0.3$). We correlate the positions of galaxies in the $j_{rm stars}$-stellar mass plane at $z=0$ with their merger history, and find that galaxies of low spins suffered dry mergers, while galaxies of normal/high spins suffered predominantly wet mergers, if any. The radial $j_{rm stars}$ profiles of galaxies that went through dry mergers are deficient by $approx 0.3$~dex at $rlesssim 10,r_{50}$ (with $r_{50}$ being the half-stellar mass radius), compared to galaxies that went through wet mergers. Studying the merger remnants reveals that dry mergers reduce $j_{rm stars}$ by $approx 30$%, while wet mergers increase it by $approx 10$%, on average. The latter is connected to the build-up of the bulge by newly formed stars of high rotational speed. Moving from minor to major mergers accentuates these effects. When the spin vectors of the galaxies prior to the dry merger are misaligned, $j_{rm stars}$ decreases to a greater magnitude, while in wet mergers co-rotation and high orbital angular momentum efficiently spun-up galaxies. We predict what would be the observational signatures in the $j_{rm stars}$ profiles driven by dry mergers: (i) shallow radial profiles and (ii) profiles that rise beyond $approx 10,r_{50}$, both of which are significantly different from spiral galaxies.
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