Godfrey died in 1100. His kinsman, Baldwin, was called down from Edessa. A papal representative crowned Baldwin King of Jerusalem on Christmas Day, 1100. Edessa was already his, but it was a separate state. Antioch and Tripoli in theory recognized Jerusalem as their superior, but in actual practice they went their own way. The Christians were no better than the Muslims at creating stable, central governments.
In sharp contrast to Europe, the nobles in Outremer (literally, beyond the sea) mainly lived in the cities. They soon set to work building castles, but the greater number of "Franks" were city dwellers. The countryside remained Arab Muslim (or, certain areas, Syrian Christian). The Franks were always a tiny minority, but their military prowess was respected and feared.
Still, the Latin Kingdom of Jerusalem survived as much through Muslim disunity as through Frankish arms. Time and again the Muslims produced a great leader who united them (or some of them, at least) -- Zengi, Nuradin, Saladin, Baybars, Kulavan -- and every time these leaders were able to push the Christians back. But, every time save the final, rivals within the Muslim world emerged and the great leaders had to turn their attentions elsewhere, and Outremer was preserved for another generation.