[Galaxy Tab 10.1 Q&A, Help & Troubleshooting] trbayth:
I did a little looking around. I have a rooted 4G LTE but with the stock ROM.

My update was in /cache and was called 86bb1913cfe9.update.bin. It's a zip file so you can pull it with adb, rename it, then unzip it. The update script looks like it's verifying each file plus the recovery plus the boot to make sure they are the original files. It updates the radio, then patches each file (not just replacing with new versions.) It also deletes some files (that shouldn't have been included in the retail build?), and adds a few new ones. Then it updates recovery and boot.

Here's the first part:

mount("ext4", "EMMC", "/dev/block/mmcblk0p4", "/system");
assert(file_getprop("/system/build.prop", "ro.build.fingerprint") == "samsung/SCH-I905/SCH-I905:3.1/HMJ37/EG01:user/release-keys" ||
file_getprop("/system/build.prop", "ro.build.fingerprint") == "samsung/SCH-I905/SCH-I905:3.1/HMJ37/EH04:user/release-keys");
assert(getprop("ro.product.device") == "SCH-I905" ||
getprop("ro.build.product") == "SCH-I905");
ui_print("Verifying current system...");
show_progress(0.100000, 0);
assert(apply_patch_check("/system/app/AngryGPS.apk", "f83190da0a30b15b3652b84dbffcde99bbdb6dd9", "61b30e6f16feb44aa454f451ce7a998300a1df40"));
set_progress(0.000347);
assert(apply_patch_check("/system/app/AngryGPS.odex", "5225f46ea76215434812deca94de5404370ea2d0", "6ea9c477c5ac7d78076a5b14193d7e8f2a91cc29"));
set_progress(0.000865);

Here's the first part of the update part:

show_progress(0.800000, 0);
ui_print("Updating CP Modem...");
assert(package_extract_file("modem_delta.bin", "/tmp/modem_delta.bin"),
p4lte_update_cdma_bp("/tmp/modem_delta.bin", "modem_delta.bin"),
delete("/tmp/modem_delta.bin"));
set_progress(0.001027);
ui_print("Removing unneeded files...");
delete("/system/app/VZWAPNLib.apk", "/system/app/VZWAPNService.apk",
"/system/app/VZWSaSSOClient.apk", "/system/bin/ip6tables",
"/system/etc/permissions/vzwapnlib.xml", "/system/lib/libmotricity.so",
"/system/framework/am.jar", "/system/framework/android.policy.jar",
"/system/framework/android.test.runner.jar",
"/system/framework/bmgr.jar", "/system/framework/bouncycastle.jar",
"/system/framework/com.android.location.provider.jar",
"/system/framework/core-junit.jar", "/system/framework/ime.jar",
"/system/framework/input.jar", "/system/framework/javax.obex.jar",
"/system/framework/monkey.jar", "/system/framework/pm.jar",
"/system/framework/sec_feature.jar", "/system/framework/seccamera.jar",
"/system/framework/sechardware.jar",
"/system/framework/secmediarecorder.jar",
"/system/framework/services.jar", "/system/framework/sqlite-jdbc.jar",
"/system/framework/svc.jar", "/system/default.prop",
"/system/recovery.img");
ui_print("Patching system files...");
apply_patch("/system/app/AngryGPS.apk", "-",
f83190da0a30b15b3652b84dbffcde99bbdb6dd9, 67746,
61b30e6f16feb44aa454f451ce7a998300a1df40, package_extract_file("patch/system/app/AngryGPS.apk.p"));
set_progress(0.001372);
apply_patch("/system/app/AngryGPS.odex", "-",
5225f46ea76215434812deca94de5404370ea2d0, 100984,
6ea9c477c5ac7d78076a5b14193d7e8f2a91cc29, package_extract_file("patch/system/app/AngryGPS.odex.p"));
set_progress(0.001886);
apply_patch("/system/app/ApplicationsProvider.apk", "-",
5d9d5fad16ee9fc3c97d97e3857680d287ca4db7, 6112,
0050f2088acd33de7bec7ab06d219bfaac77376c, package_extract_file("patch/system/app/ApplicationsProvider.apk.p"));
set_progress(0.001917);
apply_patch("/system/app/ApplicationsProvider.odex", "-",
f3b58b003aadfb1e930313099e7f41a0c50732ff, 23592,
379aaba5085bfb4ccc76b1fc49de07d5fcebd974, package_extract_file("patch/system/app/ApplicationsProvider.odex.p"));

And here's the end:

ui_print("Patching LTE image...");
apply_patch("EMMC:/dev/block/mmcblk0p9:10747904:48b8ffc6c66d5e0487ed822b28e144be69e176e1:10747904:cbbc8fb2b864c5513513ccce5aa35bced0e443a3",
"-", cbbc8fb2b864c5513513ccce5aa35bced0e443a3, 10747904,
48b8ffc6c66d5e0487ed822b28e144be69e176e1, package_extract_file("patch/lte.img.p"));
set_progress(0.979318);
ui_print("Patching boot image...");
apply_patch("EMMC:/dev/block/mmcblk0p3:4050944:21bf2e3576ddb89d0eb94ce7103a1e1c9c5c7bfe:4061184:bec5b9c1d11ff42d2a313913c33637c222ee38bf",
"-", bec5b9c1d11ff42d2a313913c33637c222ee38bf, 4061184,
21bf2e3576ddb89d0eb94ce7103a1e1c9c5c7bfe, package_extract_file("patch/boot.img.p"));
set_progress(1.000000);
delete("/system/recovery-from-boot.p",
"/system/etc/install-recovery.sh");
show_progress(0.100000, 10);
ui_print("Unpacking new files...");
package_extract_dir("system", "/system");
ui_print("Unpacking new recovery...");
package_extract_dir("recovery", "/system");
ui_print("Symlinks and permissions...");

If I shouldn't have posted that mods feel free to delete or modify it as necessary.

trb-