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We construct the moduli stack of properly balanced vector bundles onsemistable curves and we determine explicitly its Picard group. As aconsequence, we obtain an explicit description of the Picard groups of theuniversal moduli stack of vector bundles on smooth curves and of the Schmitt'scompactification over the stack of stable curves. We prove some results aboutthe gerbe structure of the universal moduli stack over its rigidification bythe natural action of the multiplicative group. In particular, we givenecessary and sufficient conditions for the existence of Poincar\'e bundlesover the universal curve of an open substack of the rigidification,generalizing a result of Mestrano-Ramanan.

The Picard group of the universal moduli space of vector bundles on stable curves