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We fit the multi-band lightcurves of 40 fast blue optical transients (FBOTs)with the magnetar engine model. The mass of the FBOT ejecta, the initial spinperiod and polar magnetic field of the FBOT magnetars are respectivelyconstrained to $M_{\rm{ej}}=0.18^{+0.52}_{-0.13}\,M_\odot$,$P_{\rm{i}}=9.4^{+8.1}_{-3.9}\,{\rm{ms}}$, and $B_{\rmp}=7^{+16}_{-5}\times10^{14}\,{\rm{G}}$. The wide distribution of the value of$B_{\rm p}$ spreads the parameter ranges of the magnetars from superluminoussupernovae (SLSNe) to broad-line Type Ic supernovae (SNe Ic-BL; some areobserved to be associated with long-duration gamma-ray bursts), which are alsosuggested to be driven by magnetars. Combining FBOTs with the other transients,we find a strong universal anti-correlation as$P_{\rm{i}}\propto{M_{\rm{ej}}^{-0.45}}$, indicating them could share a commonorigin. To be specific, it is suspected that all of these transients originatefrom collapse of extreme-stripped stars in close binary systems, but withdifferent progenitor masses. As a result, FBOTs distinct themselves by theirsmall ejecta masses with an upper limit of ${\sim}1\,M_\odot$, which leads toan observational separation in the rise time of the lightcurves $\sim12\,{\rmd}$. In addition, the FBOTs together with SLSNe can be separated from SNe Ic-BLby an empirical line in the $M_{\rm peak}-t_{\rm rise}$ plane corresponding toan energy requirement of a mass of $^{56}$Ni of $\sim0.3M_{\rm ej}$, where$M_{\rm peak}$ is the peak absolute magnitude of the transients and $t_{\rmrise}$ is the rise time.

Magnetar Engines in Fast Blue Optical Transients and Their Connections with SLSNe, SNe Ic-BL, and lGRBs