How does the no-fault divorce law apply to desertion by one party over four years ago? Have had no contact with husband who lives in austria for over four years. No address or telephone number for him. There are no children or property and no alimony is sought.

What you referred to as "desertion" has nothing to do with no-fault divorce in California. The whole point of no-fault is you don't need to prove grounds for a dissolution of marriage other than to allege irreconcilable differences, which is subject to an extremely low burden of proof.

If your marriage has failed because your husband has disappeared or abandoned you, you simply have irreconcilable differences in your marriage (to put it mildly) and may obtain a divorce if you like. That's it.

All you need to do is file a case and try to locate your husband to serve him. But that's the major problem in your case: service of process. You may need to hire a private investigator who can give you a declaration to submit to the court of your efforts at locating your husband. But the problem is compounded by the fact that your husband was last known to be in Austria. To do it right you need to find a lawyer who is experienced in service of process in other countries (there's a Hague Convention treaty controlling service outside of the US). Service by publication in the US is probably not going to make it with most judges so you're really going to have to research how this is done in a European country. If you cannot locate your husband in Austria, can you serve him there under the Hague Convention by publication? I honestly don't know which is why you really need to find someone who's handled overseas service of process cases. That's what is going to be difficult and expensive. Beyond that, everything else in your case is an easy as falling off a log. The case will probably go by default once you effect service anyway.