Selecting an alternative legal service provider (ALSP), which will often deploy technology more broadly than most law firms, can conjure fears straight out of a 1980s sci-fi film.

"You're putting your case in the hands of a machine, where you really don't know how good it is," says Bassi Edlin Huie & Blum partner Noel Edlin. "So that always makes me nervous, maybe I've seen too many 'Terminator' movies."

But seeing no Sarah Connor in sight, more corporate legal departments and law firms are seeking out ALSPs for business consultancy, legal process outsourcing, contract services, and tech-powered document analysis, among other services.