The intimate kinship basis of minuscule hunter-gatherer communities extends to non-humans, who are often regarded as kin of sorts rather than as different sorts of persons. This paper addresses the limits of approaching the worlds of hunter-gatherers starting from the binary terms « egalitarian » and « hierarchical ». These concepts impose onto their communities economic and political modern issues, as well as the notion that society is constitutive of commensurate individuals who can be compared and evaluated, and thus be regarded as equal (or not). I argue here that hunter-gatherers form more-than-human « kinship communities » composed of multiply-connected and incommensurate heterogeneous members. Hunter-gatherers figure society in a local kinship idiom, where their sense of kinship approximates what the term would signify if we read its suffix -ship as « skill » (as in horsemanship) rather than « position » (as in dictatorship). Their kinship communities subsist in skillful connection-work, which involves an open-ended network whose various members are constituted by participative cooperation itself. The end of « egalitarianism », I propose, opens our attention to a hunter-gatherer connective alternative, a « peer-to-peer » connected cosmos.