We present the results from a sensitive X-ray survey of 26 nearby hydrogen-poor superluminous supernovae (SLSNe-I) with Swift, Chandra and XMM. This dataset constrains the SLSN evolution from a few days until ~2000 days after explosion, reaching a luminosity L_x~10^40 erg/s and revealing the presence of significant X-ray emission at the location of PTF12dam. No SLSN-I is detected above L_x~10^41 erg/s, suggesting that the luminous X-ray emission L_x~10^45 erg/s associated with SCP60F6 is not common among SLSNe-I. We constrain the presence of off-axis GRB jets, ionization breakouts from magnetar central engines and the density in the sub-pc environments of SLSNe-I through Inverse Compton emission. The deepest limits rule out the weakest uncollimated GRB outflows, suggesting that IF the similarity of SLSNe-I with GRB/SNe extends to their fastest ejecta, then SLSNe-I are either powered by energetic jets pointed far away from our line of sight theta>30 deg, or harbor failed jets that do not successfully break through the stellar envelope. Furthermore, IF a magnetar central engine is responsible for the exceptional luminosity of SLSNe-I, our X-ray analysis favors large magnetic fields B>2x10^(14) G and ejecta masses M_ej>3 Msun in agreement with optical/UV studies. Finally, we constrain the pre-explosion mass-loss rate of stellar progenitors of SLSNe-I. For PTF12dam we infer Mdot<2x10^(-5) Msun/yr, suggesting that the SN shock interaction with the CSM is unlikely to supply the main source of energy powering the optical transient and that some SLSN-I progenitors end their life as compact stars surrounded by a low-density medium similar to long GRBs and Type Ib/c SNe.
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