The BLM protects BLM land. In areas where the BLM land consists of small parcels that are isolated from each other they contract the fire protection to Cal Fire. There is very little BLM land in the Central Valley. Much of the Valley is not in the SRA, so counties and municipalities provide fire protection. These areas are called the Local Responsibility Areas (LRA). The Central California District of the BLM has one fire station west of Bakersfield, but most of its land is located east of Bakersfield up to the Sierra Crest, where the BLM's California Desert District's western boundary exists. If you explore the Cal Fire site or just do a Google search you can find maps of the entire state showing the jurisdictions across the state. There are also 18 National Forests in California which form a portion of the FRA, Federal Responsibility Area. There are 3 National Parks with significant acreage, those being Sequoia-Kings Canyon, Yosemite and Lassen Volcanic. I think Pinnacles National Park contracts with Cal FIre, but I'm not sure of their latest developments. The southern California Parks are largely desert, but Joshua Tree and Mojave both have fire organizations. I'm not sure if Death Valley NP has a fire organization or apparatus. I think not, I believe the Ridgecrest Field Office of the BLM provides fire protection for Death Valley. They really don't have much wildland fuel across the majority of the park.
The juxtaposition of the FRA, SRA and LRA in the state is complex, but believe me every piece of land is in the CAD (computer assisted dispatch) of every jurisdiction's computer. There are a ton of mutual aid agreements and where two jurisdictions border each other two agencies may be on the response. For example on the Sierra National Forest the land just uphill of the Forest boundary may find Cal Fire responding along with Sierra NF units. Just below the Forest boundary you will, of course, find Cal Fire responding along with Sierra NF units. Every response area has a prescribed response, which every agency has reviewed to see what will be on the response given various levels of fire danger/weather conditions.
Somewhere on the Cal Fire website are links to a county by county map or maps showing the jurisdictions at a more readable scale than the statewide map. I don't have any saved links to aid you in finding these maps. If you want a bird's eye view of every parcel of land's jurisdiction these county maps are essential.