Does a successful call to send() with the number returned equal to the amount specified in the size parameter guarantee that no \"partial sends\" will occur?
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Though this depends on the protocol you are using, the general question is no.
For TCP the data gets buffered inside the kernel and then sent out at the discretion of the TCP packetization algorithm, which is pretty hairy - it keeps multiple timers, minds path MTU trying to avoid IP fragmentation.
For UDP you can only assume this kind of "atomicity" if your datagram does not exceed link frame size (usual value is 1472 = 1500 of ethernet frame - 20 bytes of IP header - 8 bytes of UDP header). Otherwise your sending host will have to IP-fragment the datagram.
Then intermediate routers can still IP-fragment the passing packet if their outgoing link MTU is less then the packet size.