  In this work we investigate partial actions of a Hopf algebra H on nonunital
algebras and the associated partial smash products. We show that our partial
actions correspond to nonunital algebras in the category of partial
representations of H. The central problem of existence of a globalization for a
partial action is studied in detail, and we provide sufficient conditions for
the existence (and uniqueness) of a minimal globalization for associative
algebras in general. Extending previous results by Abadie, Dokuchaev, Exel and
Simon, we define Morita equivalence for partial Hopf actions, and we show that
if two symmetrical partial actions are Morita equivalent then their standard
globalizations are also Morita equivalent. Particularizing to the case of a
partial action on an algebra with local units, we obtain several strong results
on equivalences of categories of modules of partial smash products of algebras
and partial smash products of k-categories.
