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I am interested in tracing through an upload process to learn more detail ...

I covered the uploading process in some detail here: What happens when code is uploaded using the bootloader?

I would like to understand which C-libraries are used

See my post about How the IDE organizes things

One example that I would like to see is an direct upload of C or C++ code without using the IDE gui.

I wrote a simple Makefile on the Arduino Forum:

#
# Simple Arduino Makefile
#
# Author: Nick Gammon
# Date: 18th March 2015

# where you installed the Arduino app
ARDUINO_DIR = C:/Documents and Settings/Nick/Desktop/arduino-1.0.6/

# various programs
CC = "$(ARDUINO_DIR)hardware/tools/avr/bin/avr-gcc"
CPP = "$(ARDUINO_DIR)hardware/tools/avr/bin/avr-g++"
AR = "$(ARDUINO_DIR)hardware/tools/avr/bin/avr-ar"
OBJ_COPY = "$(ARDUINO_DIR)hardware/tools/avr/bin/avr-objcopy"

MAIN_SKETCH = Blink.cpp

# compile flags for g++ and gcc

# may need to change these
F_CPU = 16000000
MCU = atmega328p

# compile flags
GENERAL_FLAGS = -c -g -Os -Wall -ffunction-sections -fdata-sections -mmcu=$(MCU) -DF_CPU=$(F_CPU)L -MMD -DUSB_VID=null -DUSB_PID=null -DARDUINO=106
CPP_FLAGS = $(GENERAL_FLAGS) -fno-exceptions
CC_FLAGS  = $(GENERAL_FLAGS)

# location of include files
INCLUDE_FILES = "-I$(ARDUINO_DIR)hardware/arduino/cores/arduino" "-I$(ARDUINO_DIR)hardware/arduino/variants/standard"

# library sources
LIBRARY_DIR = "$(ARDUINO_DIR)hardware/arduino/cores/arduino/"

build:
    
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(MAIN_SKETCH) -o $(MAIN_SKETCH).o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)avr-libc/malloc.c -o malloc.c.o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)avr-libc/realloc.c -o realloc.c.o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)WInterrupts.c -o WInterrupts.c.o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring.c -o wiring.c.o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring_analog.c -o wiring_analog.c.o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring_digital.c -o wiring_digital.c.o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring_pulse.c -o wiring_pulse.c.o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)wiring_shift.c -o wiring_shift.c.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)CDC.cpp -o CDC.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)HardwareSerial.cpp -o HardwareSerial.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)HID.cpp -o HID.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)IPAddress.cpp -o IPAddress.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)main.cpp -o main.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)new.cpp -o new.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)Print.cpp -o Print.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)Stream.cpp -o Stream.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)Tone.cpp -o Tone.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)USBCore.cpp -o USBCore.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)WMath.cpp -o WMath.cpp.o
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)WString.cpp -o WString.cpp.o
    rm core.a
    $(AR) rcs core.a malloc.c.o
    $(AR) rcs core.a realloc.c.o
    $(AR) rcs core.a WInterrupts.c.o
    $(AR) rcs core.a wiring.c.o
    $(AR) rcs core.a wiring_analog.c.o
    $(AR) rcs core.a wiring_digital.c.o
    $(AR) rcs core.a wiring_pulse.c.o
    $(AR) rcs core.a wiring_shift.c.o
    $(AR) rcs core.a CDC.cpp.o
    $(AR) rcs core.a HardwareSerial.cpp.o
    $(AR) rcs core.a HID.cpp.o
    $(AR) rcs core.a IPAddress.cpp.o
    $(AR) rcs core.a main.cpp.o
    $(AR) rcs core.a new.cpp.o
    $(AR) rcs core.a Print.cpp.o
    $(AR) rcs core.a Stream.cpp.o
    $(AR) rcs core.a Tone.cpp.o
    $(AR) rcs core.a USBCore.cpp.o
    $(AR) rcs core.a WMath.cpp.o
    $(AR) rcs core.a WString.cpp.o
    $(CC) -Os -Wl,--gc-sections -mmcu=$(MCU) -o $(MAIN_SKETCH).elf $(MAIN_SKETCH).o core.a -lm
    $(OBJ_COPY) -O ihex -j .eeprom --set-section-flags=.eeprom=alloc,load --no-change-warnings --change-section-lma .eeprom=0 $(MAIN_SKETCH).elf $(MAIN_SKETCH).eep
    $(OBJ_COPY) -O ihex -R .eeprom $(MAIN_SKETCH).elf $(MAIN_SKETCH).hex

There are quite a few more complex ones around.

I want to see kind of the "bare-minimum" necessary for programming the Arduino (in C/C++).

Here:

int main ()
 {
 }

Does part of the main sketch transfer through in the compilation of malloc.c and realloc.c (as well as the c/c++ files)?

I would think so, being that it is compiled every time we change the main sketch.

I'm not sure I understand the part about "transfer through" but basically functions which are needed in the main sketch are linked into the combined file by the linker.

Effectively these are the main parts:

# Compile main sketch
    $(CPP) $(CPP_FLAGS) $(INCLUDE_FILES) $(MAIN_SKETCH) -o $(MAIN_SKETCH).o

# Compile libraries
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)avr-libc/malloc.c -o malloc.c.o
    $(CC) $(CC_FLAGS) $(INCLUDE_FILES) $(LIBRARY_DIR)avr-libc/realloc.c -o realloc.c.o
...

# Remove temporary "combined libraries" file
    rm core.a

# Add compiled libraries into combined file "core.a"
    $(AR) rcs core.a malloc.c.o
    $(AR) rcs core.a realloc.c.o
...

# Link main sketch to combined libraries (linker will discard things not needed)
    $(CC) -Os -Wl,--gc-sections -mmcu=$(MCU) -o $(MAIN_SKETCH).elf $(MAIN_SKETCH).o core.a -lm

# Make an .eep (EEPROM) file
    $(OBJ_COPY) -O ihex -j .eeprom --set-section-flags=.eeprom=alloc,load --no-change-warnings --change-section-lma .eeprom=0 $(MAIN_SKETCH).elf $(MAIN_SKETCH).eep

# Make the main .hex file
    $(OBJ_COPY) -O ihex -R .eeprom $(MAIN_SKETCH).elf $(MAIN_SKETCH).hex

Lastly, how is the outputted .hex file uploaded to the board?

There are various ways of achieving this. The IDE calls the program avrdude which is designed to upload a .hex file to a processor. You can also just copy the .hex file to an SD card and upload it using a board programmer.