Jeremy London -- Charged with Domestic Battery, Officially Described as Homeless

Jeremy London has formally been charged with domestic battery for allegedly beating up his baby mama in Palm Springs last month -- but the crazy part ... legal docs filed in the case describe the actor as homeless.

Jeremy still hasn't been arrested for the incident -- so in addition to charging documents, authorities filed a request for an arrest warrant, describing Jeremy's alleged attack on his estranged wife Melissa Cunningham.

According to the docs, the fight started when London put the couple's son in his car to go to breakfast, but Melissa objected ... insisting the boy did not want to go.

According to the papers, an argument erupted, culminating with London pulling Melissa's hair and hitting her on the side of the head.

At the end of the documents, Jeremy is described as having no address ... simply "transient."