Context. Hydrogen-rich superluminous supernovae (SLSNe II) are rare. The exact mechanism producing their extreme light curve peaks is not understood. Analysis of single events and small samples suggest that circumstellar material (CSM) interaction is the main mechanism responsible for the observed features. However, other mechanisms cannot be discarded. Large sample analysis can provide clarification. Aims. We aim to characterize the light curves of a sample of 107 SLSNe II to provide valuable information that can be used to validate theoretical models. Methods. We analyzed the gri light curves of SLSNe II obtained through ZTF. We studied the peak absolute magnitudes and characteristic timescales. When possible, we computed the g − r colors and pseudo-bolometric light curves, and estimated lower limits for their total radiated energy. We also studied the luminosity distribution of our sample and estimated the fraction that would be observable by the LSST. Finally, we compared our sample to other H-rich SNe and to H-poor SLSNe I. Results. SLSNe II are heterogeneous. Their median peak absolute magnitude is ∼ − 20.3 mag in optical bands. Their rise can take from ∼two weeks to over three months, and their decline times range from ∼twenty days to over a year. We found no significant correlations between peak magnitude and timescales. SLSNe II tend to show fainter peaks, longer declines, and redder colors than SLSNe I. Conclusions. We present the largest sample of SLSN II light curves to date, comprising 107 events. Their diversity could be explained by different CSM morphologies, although theoretical analysis is needed to explore alternative scenarios. Other luminous transients, such as active galactic nuclei, tidal disruption events or SNe Ia-CSM, can easily become contaminants. Thus, good multiwavelength light curve coverage becomes paramount. LSST could miss ∼30% of the ZTF events in its gri band footprint.