The existence of a scaling network of current-carrying cosmic strings in our Universe is expected to continuously create loops endowed with a conserved current during the cosmological expansion. These loops radiate gravitational waves and may stabilise into centrifugally supported configurations. We show that this process generates an irreducible population of vortons which has not been considered so far. In particular, we expect vortons to be massively present today even if no loops are created at the time of string formation. We determine their cosmological distribution, and estimate their relic abundance today as a function of both the string tension and the current energy scale. This allows us to rule out new domains of this parameter space. At the same time, given some conditions on the string current, vortons are shown to provide a viable and original dark matter candidate, possibly for all values of the string tension. Their mass, spin and charge spectrum being broad, vortons would have an unusual phenomenology in dark matter searches.
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