We present mid-IR spectral decomposition of a sample of 48 Spitzer -selected ULIRGs spanning z \sim 1 – 3 and likely L _ { IR } \sim 10 ^ { 12 } – 10 ^ { 13 } L _ { \odot } . Our study aims at quantifying the star-formation and AGN processes in these sources which recent results suggest have evolved strongly between the observed epoch and today . To do this , we study the mid-IR contribution of PAH emission , continuum , and extinction . About 3/4 of our sample are continuum- ( i.e . AGN ) dominated sources , but \sim 60 % of these show PAH emission , suggesting the presence of star-formation activity . These sources have redder mid-IR colors than typical optically-selected quasars . About 25 % of our sample have strong PAH emission , but none are likely to be pure starbursts as reflected in their relatively high 5 \mu m hot dust continua . However , their steep 30 \mu m – to – 14 \mu m slopes suggest that star-formation might dominate the total infrared luminosity . Six of our z \sim 2 sources have EW _ { 6.2 } \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle > $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 0.3 \mu m and L _ { 14 \mum } \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle > $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 10 ^ { 12 } L _ { \odot } ( implying L _ { IR } \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle > $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 10 ^ { 13 } L _ { \odot } ) . At these luminosities , such high EW _ { 6.2 } ULIRGs do not exist in the local Universe . We find a median optical depth at 9.7 \mu m of \langle \tau _ { 9.7 \mum } \rangle = 1.4 . This is consistent with local IRAS -selected ULIRGs , but differs from early results on SCUBA-selected z \sim 2 ULIRGs . Similar to local ULIRGs about 25 % of our sample show extreme obscuration ( \tau _ { 9.7 \mum } \mathrel { \raise 1.505 pt \hbox { $ \scriptstyle > $ } \kern - 6.0 pt \lower 1.72 pt \hbox { { $% \scriptstyle \sim$ } } } 3 ) suggesting buried nuclei . In general , we find that our sources are similar to local ULIRGs , but are an order of magnitude more luminous . It is not clear whether our z \sim 2 ULIRGs are simply scaled-up versions of local ULIRGs , or subject to fundamentally different physical processes .