We extend ultragraph shift spaces and the realization of C*-algebras as partial crossed products to include ultragraphs with sinks (under a mild condition, called (RFUM2), which allow us dismiss use filters) we describe associated transformation groupoid. Using these characterizations study continuous orbit equivalence (via groupoids) KMS ground states products).

There are two established gradings on Leavitt path algebras associated with ultragraphs, namely the grading by integers group and free edges. In this paper, we characterize properties of these in terms underlying combinatorial ultragraphs. More precisely, when strong or epsilon-strong. The results regarding edges new also context graphs. Finally, describe relationship between strongness integer...