  The gravitational decoupling is applied to studying minimal geometric
deformed (MGD) compact superfluid stars, in covariant logarithmic scalar
gravity on fluid branes. The brane finite tension is shown to provide more
realistic values for the asymptotic value of the mass function of MGD
superfluid stars, besides constraining the range of the self-interacting scalar
field, minimally coupled to gravity. Several other physical features of MGD
superfluid stars, regulated by the finite brane tension and a decoupling
parameter, are derived and discussed, with important corrections to the
general-relativistic limit that corroborate to current observational data.
