The detection of an unexpected $sim 2.5 M_{odot}$ component in the gravitational wave event GW190814 has puzzled the community of High-Energy astrophysicists, since in the absence of further information it is not clear whether this is the heaviest neutron star ever detected or either the lightest black hole known, of a kind absent in the local neighbourhood. We show in this work a few possibilities for a model of the former, in the framework of three different quark matter models with and without anisotropy in the interior pressure. As representatives of classes of exotic solutions, we show that even though the stellar sequences may reach this ballpark, it is difficult to fulfill simultaneously the constraint of the radius as measured by the NICER team for the pulsar PSR J0030+0451. Thus, and assuming both measurements stand, compact neutron stars can not be all made of self-bound quark matter, even within anisotropic solutions which boost the maximum mass well above the $sim 2.5 M_{odot}$ figure. We also point out that a very massive compact star will limit the absolute maximum matter density in the present Universe to be less than 6 times the nuclear saturation value.
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