MD11 Captain experiences center engine anti ice failure during descent in icing conditions and elects to divert to an alternate free of icing conditions.

Narrative

Our flight was uneventful until descending into ZZZ. At approximately 14;000 we encountered icing conditions (ice rapidly forming on windshield) and selected Anti-Ice on. We received a level 1 'ENG 2 A-ICE OFF' Alert. We ran the appropriate checklist and gave Dispatch a call on SATCOM. While the IRO gave Dispatch the details of our situation; I worked with ATC to find an altitude which departed the icing conditions. We had to climb-but found an area between the cloud layers. During this time I asked the IRO to have the Dispatcher contact a Flight Qualified Supervisor so we could discuss our options. As I recall; the weather in ZZZ was 300 Overcast and light rain / drizzle. PIREP reported moderate icing below 3000' by a Caravan. Our alternate was ZZZ1. The weather was good -10000' overcast and greater than 10 miles visibility. I also asked Center about ZZZ1 icing conditions. Center called ZZZ1 Tower and told us 'No Icing in ZZZ1 area-and no icing reports in the last hour '. When the Supervisor came on the radio; I spoke with him about our flight. I recall him saying that; 'it's your decision and I will back you up with your decision. But you might want to consider coming to ZZZ; turn the Auto Throttles off; pull #2 engine back to idle to minimize damage and use if necessary '. We then spoke briefly about stabilized approach criteria and possible engine damage from ice ingestion. After weighing all the options; we decided that the safest course of action was to divert to our alternate ZZZ1. We descended from our cruise altitude; clear of clouds; for an uneventful landing in ZZZ1. I think that our crew made a good decision using excellent CRM.