In a previous article (R. Kim 2010), it was claimed largely on the basis of Tocharian that PIE simple thematic presents originally alternated between full- and zero-grade of the root.
This claim is hereby retracted, since the Tocharian facts can be explained starting from the generally accepted reconstruction of PIE verbal inflection. As argued persuasively by Peyrot (2013), Tocharian s-presents go back to PIE presents in *-sk̂é/ó-, so the reflex of zero-grade root ablaut is entirely expected.
As for TB /pər-ə/e-/, TA pär(a)- 'carry', this present results from a merger of the PIE Narten present (*bhḗr- ~ *bhér- RIGHTWARDS ARROW) *bhḗr- ~ *bhr̥- and simple thematic *bhér-e/o-, with generalized zero-grade root from the former and thematic inflection from the latter.