From what age do kabuki children appear alone in other houses' productions?

A word on terms first. A kabuki child's earliest stage appearance is usually called a hatsuomemie — led on by a father or grandfather, simply shown to the audience. What follows is the hatsubutai, the formal debut at which the child takes a stage name and stands as an actor in his own right. The two are often confused, but they differ in both order and meaning, and both commonly happen very early in childhood.

With that in place: there is no set age for joining another house's production alone. Kabuki has a number of substantial children's roles — Kanshūsai in Sugawara Denju Tenarai Kagami, for instance, a child on whom the story turns — and such roles are normally cast without regard to which house the child belongs to. Whatever boundaries exist between houses, they do not operate at the level of child casting.

What decides it, then? In practice a set of things weighed together: the child's maturity — whether he can hold through a long act, whether lines can be entrusted to him — the nature of the role, and the ties between the families. The number of years comes second; the concrete judgment "this child for this role" comes first. And being raised on other houses' stages is itself the mechanism by which the kabuki world brings up its next generation. Nothing is sealed inside a bloodline. Time spent in another company, surrounded by senior actors, is the actual circuit through which the art is handed on.